Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is different than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 32 and 36 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 97.6

2 98.2

3 97.2

4 97.0

5 97.7

6 97.3

7 97.8

8 97.5

9 97.7

10 98.3

11 97.9

12 97.5

13 98.9

14 97.9

15 97.9

16 97.0

17 97.5

18 97.8

19 97.6

20 96.5

21 98.3

22 97.8

23 97.5

24 97.8

25 98.3

26 96.6

27 97.9

28 98.3

29 97.4

30 99.1

31 97.8

32 97.9

Table 2. Fans

Subject Core Body

Temperature (F)

1 107.2

2 107.5

3 106.1

4 107.7

5 107.6

6 107.4

7 106.5

8 105.4

9 106.7

10 107.0

11 107.9

12 106.0

13 106.3

14 107.9

15 107.4

16 107.1

17 106.9

18 108.3

19 105.4

20 106.1

21 107.1

22 105.8

23 106.3

24 106.4

25 106.1

26 105.9

27 105.6

28 106.8

29 108.4

30 106.5

31 106.2

32 105.4

33 108.1

34 106.0

35 106.3

36 106.1

Per Step 1 of the 5-Steps to Hypothesis Testing, choose the appropriate null and alternative hypotheses, i.e. H0 and H1, respectively, as well as the significance level, , pronounced as "alpha".

Select one:

a.

= 10%, H0: 1 = 2, H0: 1 2

b.

H0: 1 = 2, H1: 1 2, = 5%

c.

H0: 1 2, = 1%, H1: 1 = 2

d.

H1: 1 < 2, H0: 1 = 2, = 5%

show work

Question 2

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is different than those who do use electric fans, setting the level of significance at 2.5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 34 and 47 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 103.2

2 101.8

3 102.3

4 102.1

5 101.6

6 102.0

7 101.9

8 101.2

9 102.2

10 102.6

11 102.2

12 101.7

13 101.8

14 101.6

15 103.0

16 102.1

17 102.0

18 101.8

19 101.8

20 101.9

21 101.3

22 101.9

23 101.5

24 102.2

25 102.6

26 102.1

27 101.4

28 101.6

29 101.1

30 102.2

31 101.9

32 101.6

33 102.1

34 102.7

Table 2. Fans

Subject Core Body

Temperature (F)

1 106.9

2 106.5

3 108.0

4 106.8

5 106.1

6 107.8

7 106.9

8 106.9

9 107.5

10 107.1

11 106.9

12 107.3

13 107.1

14 107.8

15 106.8

16 107.2

17 107.7

18 105.5

19 106.8

20 106.4

21 106.9

22 108.2

23 106.0

24 107.4

25 107.9

26 106.5

27 105.7

28 108.6

29 106.2

30 106.5

31 107.6

32 106.1

33 108.1

34 108.0

35 107.8

36 107.3

37 106.6

38 107.5

39 106.9

40 107.7

41 106.9

42 107.9

43 107.8

44 107.8

45 107.6

46 107.3

47 107.8

Per Step 2 of the 5-Steps to Hypothesis Testing, choose the appropriate test statistic.

Select one:

a.

z = (X1 - X2) / [ Sp * (1 / n1 + 1 / n2) ], where Sp = ( [(n1 - 1) * s12 + (n2 - 1) * s22] / [n1 + n2 - 2] )

b.

t = (X - 0) / (s / n)

c.

z = (p1 - p2) / [ p * (1 - p) * (1 / n1 + 1 / n2) ], where p1 = x1 / n1, p2 = x2 / n2, p = (x1 + x2) / (n1 + n2)

d.

z = (p - p0) / (p0 * (1 - p0) / n), where p = x / n

show work

Question 3

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is different than those who do use electric fans, setting the level of significance at 2.5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 40 and 44 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 106.2

2 105.8

3 107.0

4 106.1

5 106.0

6 106.9

7 107.8

8 103.9

9 104.4

10 106.4

11 106.1

12 107.6

13 108.2

14 107.0

15 107.9

16 106.9

17 106.6

18 107.0

19 106.4

20 106.6

21 106.9

22 106.4

23 105.6

24 105.0

25 105.9

26 106.3

27 105.5

28 105.4

29 107.1

30 106.5

31 105.9

32 107.5

33 107.3

34 106.4

35 107.4

36 107.9

37 105.3

38 105.9

39 104.9

40 106.1

Table 2. Fans

Subject Core Body

Temperature (F)

1 96.8

2 96.4

3 97.0

4 97.8

5 97.6

6 97.0

7 96.7

8 97.1

9 97.2

10 96.5

11 97.0

12 97.6

13 96.3

14 97.0

15 97.3

16 96.6

17 97.1

18 97.2

19 98.1

20 97.5

21 96.9

22 97.8

23 97.2

24 95.9

25 96.9

26 96.5

27 96.5

28 96.7

29 96.0

30 97.1

31 97.1

32 96.7

33 96.7

34 97.0

35 96.7

36 95.9

37 97.3

38 96.3

39 96.9

40 97.3

41 97.1

42 96.4

43 96.9

44 96.8

Per Step 3 of the 5-Steps to Hypothesis Testing, choose the appropriate decision rule.

Select one:

a.

Accept H0 if t -2.576 or t +2.241

b.

Reject H1 if t -1.645 and z +2.576

c.

Accept H1 if z < -1.645 and t > -2.576

d.

Reject H0 if z -2.241 or z +2.241

show work

Question 4

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is different than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 50 and 32 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 101.5

2 101.4

3 102.4

4 102.9

5 104.2

6 102.7

7 102.8

8 103.6

9 103.1

10 102.1

11 104.3

12 104.4

13 101.7

14 103.0

15 101.9

16 103.5

17 103.3

18 103.3

19 102.4

20 102.5

21 102.6

22 102.8

23 102.4

24 103.8

25 102.7

26 103.1

27 102.1

28 101.6

29 102.5

30 102.3

31 102.1

32 104.5

33 102.8

34 103.3

35 102.9

36 102.2

37 102.6

38 102.8

39 102.0

40 102.4

41 100.6

42 103.3

43 102.9

44 102.5

45 102.0

46 103.1

47 101.9

48 102.9

49 102.3

50 101.7

Table 2. Fans

Subject Core Body

Temperature (F)

1 94.8

2 93.7

3 94.9

4 95.2

5 94.9

6 94.8

7 95.6

8 95.3

9 96.2

10 94.9

11 95.7

12 93.5

13 94.8

14 96.1

15 95.3

16 94.3

17 95.6

18 94.3

19 95.0

20 94.7

21 94.4

22 94.4

23 94.5

24 95.9

25 94.9

26 96.2

27 97.3

28 94.6

29 95.3

30 94.9

31 96.3

32 94.6

Per Step 4 of the 5-Steps to Hypothesis Testing, compute the test statistic using the appropriate test statistic formula. Assign groups 1 and 2 to be no fans and fans, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) do not round your numerical answer that you submit as the online grading system is designed to mark an answer correct if your response is within a given range. In other words, the system does not take into account rounding. On the other hand, rounding is preferable when formally reporting your statistical results to colleagues.

show work

Question 5

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is different than those who do use electric fans, setting the level of significance at 1% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 42 and 34 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 95.0

2 95.0

3 95.2

4 95.1

5 94.7

6 95.9

7 95.3

8 94.7

9 95.1

10 94.8

11 95.4

12 95.1

13 95.1

14 95.3

15 95.5

16 96.0

17 94.2

18 95.1

19 95.1

20 95.5

21 94.9

22 95.9

23 93.8

24 95.8

25 95.7

26 94.8

27 94.8

28 94.8

29 94.7

30 94.9

31 94.2

32 95.2

33 94.5

34 95.5

35 94.5

36 95.1

37 94.2

38 95.1

39 95.4

40 95.2

41 96.2

42 94.3

Table 2. Fans

Subject Core Body

Temperature (F)

1 110.7

2 111.5

3 110.5

4 112.3

5 110.9

6 110.4

7 110.7

8 109.4

9 109.6

10 110.9

11 110.2

12 109.3

13 111.2

14 109.6

15 111.1

16 110.2

17 111.4

18 111.0

19 112.9

20 109.4

21 110.9

22 109.5

23 110.4

24 109.1

25 110.0

26 110.4

27 111.2

28 110.5

29 110.6

30 110.9

31 112.2

32 111.2

33 109.7

34 111.8

Per Step 5 of the 5-Steps to Hypothesis Testing, choose the appropriate formal and informal conclusions. Assign groups 1 and 2 to be no fans and fans, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) in the prior question you already calculated a test statistic but on a different dataset - calculate the test statistic again using the dataset directly above in selecting the corresponding formal and informal conclusions.

Select one:

a.

We reject H1 because z -1.645 and z = -1.282, where z = -93.715. We do not have statistically significant evidence at = 10% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is different than those who do.

b.

We accept H1 because z = -1.645 or z > +1.645, where z = -93.715. We have statistically significant evidence at = 1% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is different than those who do.

c.

We do not accept H1 because z +1.282 and z > -1.645, where z = -93.715. We have statistically significant evidence at = 5% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is different than those who do.

d.

We reject H0 because z -2.576 or z +2.576, where z = -93.715. We have statistically significant evidence at = 1% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is different than those who do.

show work

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is greater than those who do use electric fans, setting the level of significance at 1% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 15 and 29 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 99.3

2 100.1

3 99.8

4 100.1

5 99.5

6 99.0

7 99.8

8 99.2

9 99.6

10 101.9

11 100.9

12 100.2

13 99.6

14 98.8

15 100.0

Table 2. Fans

Subject Core Body

Temperature (F)

1 103.0

2 103.8

3 103.6

4 102.6

5 102.2

6 103.5

7 102.2

8 102.6

9 102.0

10 102.4

11 103.1

12 103.2

13 102.6

14 102.8

15 103.1

16 102.3

17 103.4

18 102.3

19 102.6

20 102.8

21 103.1

22 102.4

23 102.8

24 103.1

25 102.3

26 102.5

27 103.2

28 103.3

29 103.3

Per Step 1 of the 5-Steps to Hypothesis Testing, choose the appropriate null and alternative hypotheses, i.e. H0 and H1, respectively, as well as the significance level, , pronounced as "alpha".

Select one:

a.

H1: 1 2, = 2.5%, H0: 1 = 2

b.

H0: 1 > 2, = 1%, H1: 1 = 2

c.

H0: 1 = 2, H0: 1 > 2, = 5%

d.

= 1%, H0: 1 = 2, H1: 1 > 2

show work

Question 7

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is greater than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 27 and 18 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 110.7

2 110.1

3 109.8

4 110.7

5 110.1

6 110.4

7 109.9

8 109.5

9 109.6

10 109.5

11 110.9

12 111.2

13 110.7

14 110.5

15 110.1

16 110.5

17 111.4

18 111.1

19 109.4

20 109.7

21 108.7

22 111.2

23 110.6

24 111.6

25 109.6

26 109.8

27 109.0

Table 2. Fans

Subject Core Body

Temperature (F)

1 107.3

2 106.0

3 106.7

4 106.2

5 106.7

6 105.9

7 107.5

8 107.5

9 106.7

10 107.3

11 107.4

12 106.4

13 105.2

14 106.2

15 106.2

16 106.3

17 106.5

18 106.1

Per Step 2 of the 5-Steps to Hypothesis Testing, choose the appropriate test statistic.

Select one:

a.

t = (X1 - X2) / [ Sp * (1 / n1 + 1 / n2) ], where Sp = ( [(n1 - 1) * s12 + (n2 - 1) * s22] / [n1 + n2 - 2] )

b.

z = (X - 0) / (s / n)

c.

z = (X1 - X2) / [ Sp * (1 / n1 + 1 / n2) ], where Sp = ( [(n1 - 1) * s12 + (n2 - 1) * s22] / [n1 + n2 - 2] )

d.

t = (X - 0) / (s / n)

show work

Question 8

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is greater than those who do use electric fans, setting the level of significance at 2.5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 16 and 20 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 107.9

2 107.0

3 109.3

4 107.3

5 109.2

6 108.3

7 109.5

8 108.7

9 108.9

10 107.4

11 107.3

12 109.9

13 109.0

14 107.6

15 110.1

16 108.8

Table 2. Fans

Subject Core Body

Temperature (F)

1 95.1

2 97.8

3 96.5

4 97.2

5 96.4

6 96.1

7 96.4

8 96.0

9 97.0

10 96.3

11 95.9

12 97.4

13 96.7

14 96.9

15 96.3

16 96.5

17 96.3

18 96.2

19 96.8

20 96.9

Per Step 3 of the 5-Steps to Hypothesis Testing, choose the appropriate decision rule.

Select one:

a.

Reject H0 if z +1.645

b.

Reject H0 if z > -2.326

c.

Reject H0 if t +2.032

d.

Accept H1 if z > -2.326

show work

Question 9

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is greater than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 16 and 22 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 103.1

2 101.3

3 102.2

4 101.2

5 101.2

6 101.2

7 101.8

8 101.9

9 102.9

10 102.3

11 102.2

12 101.9

13 101.8

14 102.4

15 102.5

16 101.9

Table 2. Fans

Subject Core Body

Temperature (F)

1 111.3

2 109.9

3 110.6

4 109.5

5 111.3

6 110.0

7 110.0

8 110.5

9 108.7

10 109.9

11 111.1

12 110.3

13 110.0

14 109.3

15 110.7

16 110.2

17 110.7

18 110.2

19 109.9

20 110.7

21 110.7

22 110.3

Per Step 4 of the 5-Steps to Hypothesis Testing, compute the test statistic using the appropriate test statistic formula. Assign groups 1 and 2 to be no fans and fans, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) do not round your numerical answer that you submit as the online grading system is designed to mark an answer correct if your response is within a given range. In other words, the system does not take into account rounding. On the other hand, rounding is preferable when formally reporting your statistical results to colleagues.

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Question 10

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true average core body temperature amidst higher ambient temperature and humidity levels for the population who do not use electric fans is greater than those who do use electric fans, setting the level of significance at 10% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 25 and 24 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature (F)

1 96.6

2 96.8

3 97.2

4 96.7

5 98.7

6 97.4

7 97.2

8 98.3

9 98.8

10 97.1

11 96.3

12 96.1

13 97.4

14 97.1

15 97.7

16 97.7

17 96.1

18 97.6

19 96.8

20 98.3

21 96.5

22 97.5

23 97.0

24 96.9

25 98.0

Table 2. Fans

Subject Core Body

Temperature (F)

1 99.3

2 99.7

3 99.6

4 101.5

5 101.2

6 101.0

7 100.7

8 101.2

9 100.3

10 100.5

11 100.1

12 100.9

13 101.1

14 102.2

15 99.4

16 100.5

17 99.4

18 100.4

19 100.5

20 99.4

21 100.2

22 102.4

23 100.4

24 98.9

Per Step 5 of the 5-Steps to Hypothesis Testing, choose the appropriate formal and informal conclusions. Assign groups 1 and 2 to be no fans and fans, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) in the prior question you already calculated a test statistic but on a different dataset - calculate the test statistic again using the dataset directly above in selecting the corresponding formal and informal conclusions.

Select one:

a.

We accept H1 because t < -1.282, where t = -13.479. We have statistically significant evidence at = 10% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is greater than those who do.

b.

We do not reject H0 because t < +1.300, where t = -13.479. We do not have statistically significant evidence at = 10% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is greater than those who do.

c.

We do not accept H1 because t -1.282, where t = -13.479. We do not have statistically significant evidence at = 1% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is greater than those who do.

d.

We reject H1 because t +1.960, where t = -13.479. We do not have statistically significant evidence at = 5% to show that the true population average core body temperature amidst higher ambient temperature and humidity levels for those who do not use an electric fan is greater than those who do.

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Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 20 and 15 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature

Increased?

1 0

2 1

3 0

4 1

5 0

6 0

7 0

8 0

9 0

10 0

11 0

12 0

13 0

14 0

15 1

16 0

17 1

18 0

19 0

20 0

Table 2. Fans

Subject Core Body

Temperature

Increased?

1 1

2 1

3 0

4 0

5 1

6 1

7 1

8 1

9 1

10 0

11 0

12 0

13 0

14 1

15 0

Per Step 1 of the 5-Steps to Hypothesis Testing, choose the appropriate null and alternative hypotheses, i.e. H0 and H1, respectively, as well as the significance level, , pronounced as "alpha".

Please note that 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health.

Select one:

a.

H1: p1 < p2, = 5%, H0: p1 = p2

b.

= 10%, H0: p1 = p2, H0: p1 p2

c.

H0: p1 = p2, = 1%, H1: p1 < p2

d.

H1: p1 p2, H0: p1 = p2, = 2.5%

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Question 12

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 1% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 16 and 25 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature

Increased?

1 0

2 0

3 0

4 0

5 0

6 1

7 0

8 1

9 0

10 0

11 0

12 1

13 0

14 0

15 0

16 1

Table 2. Fans

Subject Core Body

Temperature

Increased?

1 0

2 0

3 0

4 0

5 1

6 0

7 0

8 0

9 1

10 0

11 1

12 1

13 0

14 0

15 0

16 1

17 0

18 0

19 0

20 0

21 1

22 1

23 0

24 1

25 1

Per Step 2 of the 5-Steps to Hypothesis Testing, choose the appropriate test statistic.

Please note that 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health.

Select one:

a.

t = (X - 0) / (s / n)

b.

t = (X1 - X2) / [ Sp * (1 / n1 + 1 / n2) ], where Sp = ( [(n1 - 1) * s12 + (n2 - 1) * s22] / [n1 + n2 - 2] )

c.

z = (X - 0) / (s / n)

d.

z = (p1 - p2) / [ p * (1 - p) * (1 / n1 + 1 / n2) ], where p1 = x1 / n1, p2 = x2 / n2, p = (x1 + x2) / (n1 + n2)

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Question 13

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 10% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 40 and 23 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature

Increased?

1 1

2 0

3 1

4 1

5 0

6 0

7 1

8 0

9 0

10 0

11 0

12 0

13 0

14 0

15 0

16 0

17 0

18 0

19 0

20 0

21 0

22 0

23 0

24 0

25 1

26 0

27 0

28 0

29 0

30 0

31 0

32 0

33 0

34 1

35 0

36 0

37 0

38 0

39 0

40 1

Table 2. Fans

Subject Core Body

Temperature

Increased?

1 0

2 1

3 0

4 1

5 0

6 1

7 0

8 1

9 1

10 1

11 0

12 0

13 0

14 0

15 1

16 0

17 1

18 1

19 0

20 0

21 0

22 0

23 0

Per Step 3 of the 5-Steps to Hypothesis Testing, choose the appropriate decision rule.

Please note that 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health.

Select one:

a.

Reject H0 if z -1.282

b.

Accept H1 if t = -1.645

c.

Accept H0 if z -1.282

d.

Reject H0 if z +2.326

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Question 14

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 2.5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 17 and 42 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature

Increased?

1 0

2 1

3 0

4 0

5 0

6 1

7 0

8 0

9 1

10 0

11 1

12 1

13 1

14 0

15 1

16 0

17 1

Table 2. Fans

Subject Core Body

Temperature

Increased?

1 0

2 1

3 1

4 0

5 1

6 0

7 1

8 0

9 0

10 1

11 1

12 0

13 0

14 0

15 1

16 0

17 0

18 0

19 0

20 0

21 0

22 0

23 1

24 1

25 1

26 0

27 0

28 0

29 0

30 0

31 1

32 0

33 0

34 1

35 1

36 0

37 1

38 1

39 1

40 0

41 0

42 1

Per Step 4 of the 5-Steps to Hypothesis Testing, compute the test statistic using the appropriate test statistic formula.

Please note the following: 1) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 2) you may copy and paste the data into Excel to facilitate analysis; and 3) do not round your numerical answer that you submit as the online grading system is designed to mark an answer correct if your response is within a given range. In other words, the system does not take into account rounding. On the other hand, rounding is preferable when formally reporting your statistical results to colleagues.

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Question 15

Recall in the one sample hypothesis testing scenario that we investigated the following presumptions based on previous research, "no evidence currently exists supporting or refuting the use of electric fans during heat waves" in terms of mortality and illness, as well as Public Health guidelines suggesting not using fans during hot weather, with some research reporting the potential of fans accelerating body heating.

You decide to further your research project by hypothesizing that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans, setting the level of significance at 5% for the formal hypothesis test. In other words, you extend your sampling to two samples instead of just one. You randomly sample 37 and 31 participants for your first and second groups, respectively, based on your research funding and for 45 minutes, all study participants sit in a chamber maintained at a temperature of 108 degrees Fahrenheit (i.e., 42 degrees Celsius) and a relative humidity of 70%. After the first 45-minute warming period, you record the participants' core body temperatures. Furthermore, for Group 2 only you place a personal sized electric fan 3 feet away with its airflow directed at a given participant's chest area, and the participants relax in this position for the next 45 minutes, whereas for Group 1 you do not provide electric fans. At the end of this 45-minute fan period, you record the core body temperatures of all participants, documenting any temperature increases as compared to the start of the time period. The following table comprises the data you collect.

Table 1. No Fans

Subject Core Body

Temperature

Increased?

1 1

2 0

3 0

4 1

5 0

6 0

7 1

8 0

9 1

10 0

11 1

12 0

13 0

14 1

15 0

16 0

17 0

18 1

19 0

20 0

21 0

22 0

23 1

24 0

25 0

26 0

27 0

28 0

29 0

30 0

31 0

32 0

33 0

34 0

35 0

36 1

37 1

Table 2. Fans

Subject Core Body

Temperature

Increased?

1 0

2 0

3 0

4 0

5 0

6 0

7 1

8 0

9 0

10 0

11 0

12 0

13 0

14 0

15 0

16 0

17 0

18 1

19 1

20 0

21 0

22 0

23 0

24 0

25 0

26 1

27 0

28 0

29 0

30 0

31 1

Per Step 5 of the 5-Steps to Hypothesis Testing, choose the appropriate formal and informal conclusions.

Please note the following: 1) you may copy and paste the data into Excel to facilitate analysis; and 2) in the prior question you already calculated a test statistic but on a different dataset - calculate the test statistic again using the dataset directly above in selecting the corresponding formal and informal conclusions.

Select one:

a.

We do not reject H0 because z > +2.326, where z = 1.079. We have statistically significant evidence at = 1% to show that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans.

b.

We accept H0 because z = -2.326, where z = 1.079. We have statistically significant evidence at = 5% to show that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans.

c.

We do not accept H0 because z < -1.645, where z = 1.079. We do not have statistically significant evidence at = 2.5% to show that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans.

d.

We do not reject H0 because z > -1.645, where z = 1.079. We do not have statistically significant evidence at = 5% to show that the true proportion of core body temperature increases amidst higher ambient temperature and humidity levels for the population who do not use electric fans is less than those who do use electric fans.

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