Question 6

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

Please 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 = (X?1 - X?2) / [ Sp * ?(1 / n1 + 1 / n2) ], where Sp = ?( [(n1 - 1) * s12 + (n2 - 1) * s22] / [n1 + n2 - 2] )

b.

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

c.

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

d.

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

Please 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.

Please show work

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

b.

We do not reject H0 because t

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.

Please show work

Question 11

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.

FOF Hypothesis-Testing-Flowchart-v0.2-2017-02-03.pdf Open with Google Docs Which Hypothesis Testing Is my data Procedure do I use? Is my data Dichotomous continuous or -One sample Two samples continuous or -Dichotomous dichotomous? dichotomous? H& Pi Continuous Do I have one of Continuous two samples? (3) Hi Pi # pa Choose either (1) (2), or (3) Choose either (1), (2), or (3) Choose either (1). (21, or (3) Choose either (1). (2), or (3) "Define p in words Define y in words Do not fill th or Ary with numbers are my data Do not fill py or pa with numbers Define A, groups 1 and 2 in words define p, groups 1 and 2 in words Z= P-Po Decision Rule. Large Samples Decision Rule. Small Samples: the VP.(1-Payn For a = 0.05. For a = 0.0 1) Reject H, if z s -1 ) Reject Hoifts - p =x (2) Reject Ho if z 2 +1.645 (2) Reject He if 1 2 +ten P1 - P n (3) Reject Me if z s -1.96 or z 2 +1.96 (3) Reject He if t s -tan or 1 2 +tama Vp(1 - p)(1, + 12) where x is the Choose either (1). (21. or (3) Choose either (1). (2), or (3) corresponding to My decision orresponding to Hi decision Find tan and tau in Table 2 in the -Sample Cont- -2-Sample Conty ne-sided test a = .05" and "two-sided where x1 and x2 are the number of In Excel do: test a = .05" columns, respectively. 1-Sample Dich successes in samples 1 and 2, :=(phat - po) / SQRT( po * (1-p0) / n) 42-Sample Dich. Degrees-of-freedom (d) (a) For one sample, usedf = n - 1 b) For two samples, use of = nl + n2 - In Excel do: :=(phatl - phat2) / ( SQRT( phat * (1-phat) . (1l + 12)) Choose either (a) or (b) but not both sample size -1-Sample Cont 2-Sample Cont 2 30 or