In a hypothesis test to compare two sample groups, the sample size for each sample group is 28. The population standard deviation for each sample group is known. The appropriate technique to use is ______________

Question 1 options:

a)	one-sample z-test

b)	three-sample f-test

c)	one-sample t-test

d)	two-sample t-test

e)	two-sample z-test

Question 2

A researcher wishes to test a hypothesis that compares family incomes between two cities. He sampled 15 households from each city. He was not given the population standard deviation of family income for each city. The population standard deviations are unknown. The degree of freedom is _______

a)

14

b)

28

c)	None of the options

d)

30

e)

15

Question 3

A researcher wishes to test a hypothesis that the average family incomes in City A is more than the average family income in City B. He sampled 20 households from each city. The population standard deviation for each city is unknown. At 5% significance level, the critical value __________

a)

1.690

b)

1.650

c)

1.680

d)

1.960

e)

2.030

Question 4

A researcher wishes to test a hypothesis that the average family income in City A is less than the average family income in City B. He sampled 15 households from each city. The population standard deviation for each city is known. At 10% significance level, the critical value __________

a)

- 1.28

b)

+ 1.28

c)

- 1.313

d)

+ 1.313

e)

- 1.310

Question 5

A professor wants to know if students in his day class did better on a test than students in his night class. She obtained the following summary statistics.

	Day	Night
Sample Mean	70	66
Sample Standard Deviation	10	8
Sample Size	36	36

The test value is _________________

Question 5 options:

a)

2.550

b)	None of the options

c)

0.880

d)

1.082

e)

1.874

Question 6

A researcher is testing a research hypothesis that IQs of students from private schools is significantly higher than that of their counterparts from the public school. At 10% significant level, the p-value for the hypothesis test was 25%. The conclusion is that ________________

a)	the IQs of students from private schools is lower than their counterparts from public schools.

b)	there is a significant difference in IQs between students from private and public schools.

c)	there is no significant difference in IQs between students from private and public schools.

d)	Cannot be determined.

e)	the IQs of students from private schools is higher than their counterparts from public schools.

Question 7

The following Excel output shows the result of a hypothesis test (at alpha 5%) which explores whether there is a significant difference in crime rate between two cities - Tomville and Dinaville.

t-Test: Two-Sample Assuming Unequal Variances
	Tomsville	Dinaville
Mean	17.1	19.4
Variance	9.7	5.4
Observations	10	10
Hypothesized Mean Difference	0
df	17
t Stat	-1.90
P(T<=t) one-tail	0.04
t Critical one-tail	1.74
P(T<=t) two-tail	0.07
t Critical two-tail	2.11

Which of the following statements is a correct interpretation of the p-value?

Question 7 options:

a)	There is a 4% chance of an error if the null hypothesis is accepted

b)	There is 7% chance of an error if the null hypothesis is rejected

c)	There is 2.11% chance of an error if the null hypothesis is rejected

d)	There is 7% chance of an error if the null hypothesis is accepted

e)	There is 4% chance of an error if the null hypothesis is rejected

Question 8

The following Excel output shows the result of a hypothesis test which explores whether male drivers pay more in insurance premium than female drivers (at alpha 5%).

t-Test: Two-Sample Assuming Unequal Variances
	Male	Female
Mean	$344.10	$245.60
Variance	8681.43	6102.93
Observations	10	10
Hypothesized Mean Difference	0
df	18
t Stat	2.56
P(T<=t) one-tail	0.01
t Critical one-tail	1.74
P(T<=t) two-tail	0.02
t Critical two-tail	2.11

Which of the following is the correct interpretation of p-value?

Question 8 options:

a)	There is 2% chance of an error if the null hypothesis is rejected

b)	There is 1% chance of an error if the null hypothesis is rejected

c)	There is 5% chance of an error if the null hypothesis is rejected

d)	There is 1% chance of an error if the null hypothesis is accepted

e)	There is 1.74% chance of an error if the null hypothesis is accepted

Question 9

A city planner believes that the public transit users spend less time commuting to work than non-public transit users. He surveyed 26 public transit users and 26 non-public transit users. The public transit users have an average commuting time of 20 minutes with a standard deviation of 5 minutes. The non-public transit users have an average commuting time of 30 minutes with a standard deviation of 10 minutes. Alpha is 10%.

The alternative hypothesis is _________________

Question 9 options:

a)	Public transit users spend different amount of time commuting to work compared to non-public transit users.

b)	None of the options

c)	Public transit users spend less time commuting to work than nonpublic transit users.

d)	Public transit users spend more time commuting to work than non-public transit users.

e)	Public transit users spend the same amount of time commuting to work as non-public transit users.

Question 10

A city planner believes that the transit users spend less time commuting to work than non-transit users. He surveyed 26 public transit users and 26 non-public transit users. The public transit users have an average commuting time of 20 minutes with a standard deviation of 5 minutes. The non-public transit users have an average commuting time of 30 minutes with a standard deviation of 10 minutes. Alpha is 10%.

The critical value is _________________

Question 10 options:

a)

+ 1.676

b)

- 1.28

c)

+ 1.28

d)

- 1.299

e)

+ 1.299

Question 11

A city planner believes that the public transit users spend less time commuting to work than non-public transit users. He surveyed 26 public transit users and 26 non-public transit users. The public transit users have an average commuting time of 20 minutes with a standard deviation of 5 minutes. The non-public transit users have an average commuting time of 30 minutes with a standard deviation of 10 minutes. Alpha is 10%.

The test value is _________________

Question 11 options:

a)

-4.56

b)	None of the options

c)

- 2.08

d)

- 2.13

e)

-17.33

Question 12

A city planner believes that the public transit users spend less time commuting to work than non-public transit users. He surveyed 26 public transit users and 26 non-public transit users. The public transit users have an average commuting time of 20 minutes with a standard deviation of 5 minutes. The non-public transit users have an average commuting time of 30 minutes with a standard deviation of 10 minutes. Alpha is 10%.

The statistical decision is to _________________

Question 12 options:

a)	reject the null hypothesis, and conclude that public transit users spend more time commuting to work than non public transit users

b)	None of the options

c)	accept the null hypothesis, and conclude that public transit users spend the different amount of time commuting to work as non public transit users.

d)	reject the null hypothesis, and conclude that public transit users spend less time commuting to work than non public transit users

e)	accept the null hypothesis, and conclude that public transit users spend the same amount of time commuting to work as non public transit users.

Question 13

Which of the following test is used in ANOVA?

Question 13 options:

a)

Z-test

b)

Chi-test

c)

F-test

d)

T-test

e)

R-test

Question 14

In the ANOVA, treatments refer to __________________ Question 14 options:

a)	statistical applications.

b)	different levels of a factor.

c)	experimental units.

d)	the dependent variables.

e)	None of the options

Question 15

The two types of variability involved in the measurement outcome for ANOVA are _____________

Question 15 options:

a)	SSB and SST

b)	SSB and SSW

c)	SST and SSW

d)	SST and SSR

e)	None of the above

Question 16

In an ANOVA test, the within-group variation (SSW) is 1264 and between-group variation (SSB) is 408. The study involved three groups, with 10 subjects in each group. The degree of freedom for between-group variation is _________________

Question 16 options:

a)

30

b)

3

c)

27

d)

2

e)

29

Question 17

An ANOVA procedure is used for data obtained from five sample groups, and each group comprised of 25 observations. At alpha 5%, the F-critical value is _____________________

Question 17 options:

a)	None of the options

b)

2.759

c)

2.447

d)

2.088

e)

2.603

Question 18

In an analysis of variance problem if MSB = 178 and MSW = 205, then F-test value is __________

Question 18 options:

a)	None of the options

b)

2.066

c)

0.1312

d)

0.868

e)

1.152

Question 19

In an analysis of variance problem if SSW = 74 and SSB = 128, then SST is __________

Question 19 options:

a)

74

b)

54

c)

128

d)

202

e)	None of the options

Question 20

At 5% significance level, a researcher conducted an ANOVA test comparing five groups of treatments with 10 observations per group. The following is a partial ANOVA table obtained from the research.

Source	SS	df	MS	F-test	P-value	F-critical
Between Variation	224	(b)	(e)	(g)	0.002	(h)
Within Variation	(a)	(c )	(f)
Total Variation	408	(d)

The degree of freedoms for values in cell (b) and cell (c) are __________

Question 20 options:

a)

5 and 50

b)

4 and 9

c)	None of the options

d)

4 and 45

e)

5 and 10

Question 21

At 5% significance level, a researcher conducted an ANOVA test comparing five groups of treatments with 10 observations per group. The following is a partial ANOVA table obtained from the research.

Source	SS	df	MS	F-test	P-value	F-critical
Between Variation	224	(b)	(e)	(g)	0.002	(h)
Within Variation	(a)	(c )	(f)
Total Variation	408	(d)

The values for MSB (cell e) and MSW (cell f), respectively, are __________

Question 21 options:

a)	44.8 and 3.76

b)	56 and 4.09

c)	56 and 20.44

d)	None of the options

e)	44.8 and 18.4

Question 22

At 5% significance level, a researcher conducted an ANOVA test comparing five groups of treatments with 10 observations per group. The following is a partial ANOVA table obtained from the research.

Source	SS	df	MS	F-test	P-value	F-critical
Between Variation	224	(b)	(e)	(g)	0.002	(h)
Within Variation	(a)	(c )	(f)
Total Variation	408	(d)

The f-test value in cell (g) is __________

Question 22 options:

a)	None of the options

b)

13.7

c)

14.10

d)

12.77

e)

0.073

Question 23

At 5% significance level, a researcher conducted an ANOVA test comparing five groups of treatments with 10 observations per group. The following is a partial ANOVA table obtained from the research.

Source	SS	df	MS	F-test	P-value	F-critical
Between Variation	224	(b)	(e)	(g)	0.002	(h)
Within Variation	(a)	(c )	(f)
Total Variation	408	(d)

The f-critical value is cell (h) is ________

Question 23 options:

a)

2.794

b)

2.400

c)

2.579

d)

2.561

e)	None of the options

Question 24

In an Anova test, an F-test value ________________ will likely suggest that the difference between groups is the same as difference within groups.

Question 24 options:

a)	equal to 1

b)	none of the options

c)	less than 1

d)	greater than 0

e)	greater than 1

Question 25

In an Anova test, an F-test value ________________ will likely suggest that the difference between groups is more than difference within groups.

Question 25 options:

a)	equal to 0

b)	equal to 1

c)	less than 1

d)	greater than 1

e)	less than 0