Question 1

What is the null hypothesis? Use $\alpha = 0.05$.

Accepted Answer

A)  $H _ { 0 } ; \mu _ { 1 } \neq \mu _ { 2 }$ 
B)  $H _ { 0 } : \mu _ { 1 } \geq \mu _ { 2 }$ 
C)  $H _ { 0 } : \mu _ { 1 } \leq \mu _ { 2 }$ 
D)  $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ 
A)  $H _ { 0 } ; \mu _ { 1 } \neq \mu _ { 2 }$ 
B)  $H _ { 0 } : \mu _ { 1 } \geq \mu _ { 2 }$ 
C)  $H _ { 0 } : \mu _ { 1 } \leq \mu _ { 2 }$ 
D)  $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

Question 2

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.
 $$\begin{array} { | l | l | } 
\hline \text { Miles / Gal Without } & \text { Miles / Gal With } \
\hline 21.2 & 23.8 \
\hline 25.4 & 25.6 \
\hline 20.9 & 22.4 \
\hline 27.6 & 28.3 \
\hline 22.8 & 24.5 \
\hline 27.3 & 28.8 \
\hline 23.4 & 25.2 \
\hline
\end{array}$$
-A running coach wanted to see whether runners ran faster after eating spaghetti the night before a race. Twenty-four random runners were chosen for this study. They ran a 5-kilometre race after having a
Normal dinner the night before, and then a week later, re-ran the same race after having a spaghetti dinner
The night before. Their results (in seconds) are in the table below. At ${ } ^ { \ddagger } = .01$ , what is the test value for
This test? $$\begin{array} { | l | c | c | c | } 
\hline & \text { Regular Dinner } & \begin{array} { c } 
\text { Spaghetti } \
\text { Dinner }
\end{array} & \begin{array} { c } 
\text { Difference } \
\text { by Runner }
\end{array} \
\hline \text { Sample mean } & 1000 & 980 & - 20 \
\hline \text { Sample variance } & 3000 & 2800 & 400 \
\hline
\end{array}$$

Accepted Answer

A)  -3.41 
B)  -1.00 
C)  -0.26 
D)  -4.90 
A)  -3.41 
B)  -1.00 
C)  -0.26 
D)  -4.90

Question 3

Joan moves into her new apartment and wants to purchase a new couch. She wants to determine if there is any difference between the average costs of couches at two different stores. Test the hypothesis that there $\text { is no difference at } \alpha=0.05 \text {. }$

$\begin{array}{|l|l|l|}
\hline & \text { Store 1 } & \text { Store 2 } \
\hline \bar{x} & \$ 650 & \$ 730 \
\hline \sigma & \$ 66 & \$ 78 \
\hline n & 24 & 21 \
\hline
\end{array}$

Accepted Answer

The answer of Joan moves into her new apartment and...

Question 4

A researcher hypothesizes that the variation in the car rental rates at a major citiy's airport is less than the car rental rates in that city. The variance of 7 airport car rental rates was $25 and the variance of 4 city car
Rental rates was $60. What is the test value?

Accepted Answer

A)  4.20 
B)  1.55 
C)  2.40 
D)  5.76 
A)  4.20 
B)  1.55 
C)  2.40 
D)  5.76

Question 5

Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town and it is believed that the average hourly wages charged by both agencies are the same. Test this claim at$a=0.05$

Accepted Answer

F-test: @#LAT-DLM& therefore it can be a

Question 6

In the figure below, if the $\mathrm { z }$-test value is $1.43$ for a test of the difference between two large sample means, then the null hypothesis should not be rejected.

Accepted Answer

A) True 
 B)False

Question 7

A recent survey reported that in a sample of 300 students who attend community colleges, 105 work at least 20 hours a week. In a sample of 225 students attending universities, only 20 students were found to
Work at least 20 hours per week. What is the test value?

Accepted Answer

A)  6.95 
B)  7.61 
C)  2.38 
D)  4.18 
A)  6.95 
B)  7.61 
C)  2.38 
D)  4.18

Question 8

Determine the $95 \%$ confidence interval of the true difference in the means. A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Use $\alpha =$$0.05$.
$\begin{array}{|l|l|l|}
\hline & \text { Africa } & \text { Asia } \
\hline \overline{\bar{X}} & 55.3 & 65.2 \
\hline \sigma & 8.1 & 9.3 \
\hline n & 53 & 42 \
\hline
\end{array}$

Accepted Answer

A)  $- 12.16 < \mu _ { 1 } - \mu _ { 2 } < - 686$ 
B)  $- 13.46 < \mu _ { 1 } - \mu _ { 2 } < - 6.34$ 
C)  $- 11.35 < \mu _ { 1 } - \mu _ { 2 } < - 7.58$ 
D)  $- 16.33 < \mu _ { 1 } - \mu _ { 2 } < - 5.98$ 
A)  $- 12.16 < \mu _ { 1 } - \mu _ { 2 } < - 686$ 
B)  $- 13.46 < \mu _ { 1 } - \mu _ { 2 } < - 6.34$ 
C)  $- 11.35 < \mu _ { 1 } - \mu _ { 2 } < - 7.58$ 
D)  $- 16.33 < \mu _ { 1 } - \mu _ { 2 } < - 5.98$

Question 9

The critical value for a two-tailed F -test is 2.65, when $a = 0.05$ , the sample size from which the variance
for the numerator was obtained = 10, and the sample size from which the variance for the denominator
was obtained = 15.

Accepted Answer

A) True 
 B)False

Question 10

If the samples are dependent, the f - test for dependent samples is used.

Accepted Answer

A) True 
 B)False

Question 11

What is the test value? Use $a = 0.05$ . (Use the variances unequal formula.)

Accepted Answer

A)  -6.97 
B)  -2.50 
C)  -4.53 
D)  -2.54 
A)  -6.97 
B)  -2.50 
C)  -4.53 
D)  -2.54

Question 12

If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

Accepted Answer

A)  reject the null hypothesis 
B)  accept the null hypothesis 
C)  reject the alternative hypothesis 
D)  not enough information 
A)  reject the null hypothesis 
B)  accept the null hypothesis 
C)  reject the alternative hypothesis 
D)  not enough information

Question 13

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.
 $$\begin{array} { | l | l | } 
\hline \text { Miles / Gal Without } & \text { Miles / Gal With } \
\hline 21.2 & 23.8 \
\hline 25.4 & 25.6 \
\hline 20.9 & 22.4 \
\hline 27.6 & 28.3 \
\hline 22.8 & 24.5 \
\hline 27.3 & 28.8 \
\hline 23.4 & 25.2 \
\hline
\end{array}$$
-Compute the standard deviation of the difference.

Accepted Answer

A)  0.78 
B)  0.69 
C)  0.87 
D)  0.48 
A)  0.78 
B)  0.69 
C)  0.87 
D)  0.48

Question 14

For normally distributed populations, if two samples are independent and the variances are known, the z -
test is used.

Accepted Answer

A) True 
 B)False

Question 15

A conservationist wants to know if the average water level(in meters) in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at $\alpha = 0.01$
$\begin{array}{|l|l|l|}
\hline & \text { Horseshoe Lake } & \text { Swan Lake } \
\hline \bar{x} & 43 & 38 \
\hline \sigma & 3.2 & 2.4 \
\hline n & 23 & 23 \
\hline
\end{array}$

Accepted Answer

@#LAT-DLM& It appears that the average w

Question 16

If the variances are not known, and one or both sample sizes are less than 30, the F -test must be
used.

Accepted Answer

A) True 
 B)False

Question 17

The formula for the $f$ - test for comparing two means (independent samples, variances equal)
$$t = \frac { \left( \bar { X } _ { 1 } - \bar { X } _ { 2 } \right) - \left( \mu _ { 1 } - \mu _ { 2 } \right) } { \sqrt { \frac { s _ { 1 } ^ { 2 } } { n _ { 1 } } + \frac { s _ { 2 } ^ { 2 } } { n _ { 2 } } } } .$$

Accepted Answer

A) True 
 B)False

Question 18

The critical value for a one-tailed right F -test is 2.57, when $$a = 0.025$$ , the degrees of freedom for the
numerator = 15, and the degrees of freedom for the denominator = 20.

Accepted Answer

A) True 
 B)False

Question 19

A conservationist wants to know if the water level (in meters) in Crab Lake is more or less variable than the water level in Gull Lake. If one tested the hypothesis that the levels are equally variable at $\alpha = 0.05$, the critical value would be

$\begin{array}{|l|l|l|}
\hline & \text { Crab Lake } & \text { Gull Lake } \
\hline \bar{x} & 44 & 3.3 \
\hline \$ & 3.9 & 2.4 \
\hline 4 & 22 & 21 \
\hline
\end{array}$

Accepted Answer

A)  2.25 
B)  2.42 
C)  2.64 
D)  2.88 
A)  2.25 
B)  2.42 
C)  2.64 
D)  2.88

Question 20

A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station
Wagons is $3,900. For $\alpha = 0.05$ what is the test value?

Accepted Answer

A)  3.00 
B)  3.04 
C)  2.78 
D)  2.33 
A)  3.00 
B)  3.04 
C)  2.78 
D)  2.33

What is the null hypothesis? Use $\alpha = 0.05$ .

A researcher hypothesizes that the variation in the car rental rates at a major citiy's airport is less than the car rental rates in that city. The variance of 7 airport car rental rates was $25 and the variance of 4 city car Rental rates was $60. What is the test value?

Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town and it is believed that the average hourly wages charged by both agencies are the same. Test this claim at $a=0.05$

A recent survey reported that in a sample of 300 students who attend community colleges, 105 work at least 20 hours a week. In a sample of 225 students attending universities, only 20 students were found to Work at least 20 hours per week. What is the test value?

The critical value for a two-tailed F -test is 2.65, when $a = 0.05$ , the sample size from which the variance for the numerator was obtained = 10, and the sample size from which the variance for the denominator was obtained = 15.

If the samples are dependent, the f - test for dependent samples is used.

What is the test value? Use $a = 0.05$ . (Use the variances unequal formula.)

If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

For normally distributed populations, if two samples are independent and the variances are known, the z - test is used.

A conservationist wants to know if the average water level(in meters) in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at $\alpha = 0.01$ Horseshoe Lake Swan Lake 43 38 \sigma 3.2 2.4 n 23 23

If the variances are not known, and one or both sample sizes are less than 30, the F -test must be used.

The critical value for a one-tailed right F -test is 2.57, when $a = 0.025$ , the degrees of freedom for the numerator = 15, and the degrees of freedom for the denominator = 20.

A conservationist wants to know if the water level (in meters) in Crab Lake is more or less variable than the water level in Gull Lake. If one tested the hypothesis that the levels are equally variable at $\alpha = 0.05$ , the critical value would be Crab Lake Gull Lake 44 3.3 \ 3.9 2.4 4 22 21

A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station Wagons is $3,900. For $\alpha = 0.05$ what is the test value?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

Exam 8: Testing the Difference Between Two Means, Two Proportions, and Two Variances

What is the null hypothesis? Use α=0.05\alpha = 0.05α=0.05 .

A researcher hypothesizes that the variation in the car rental rates at a major citiy's airport is less than the car rental rates in that city. The variance of 7 airport car rental rates was $25 and the variance of 4 city car Rental rates was $60. What is the test value?

Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town and it is believed that the average hourly wages charged by both agencies are the same. Test this claim at a=0.05a=0.05a=0.05

In the figure below, if the z\mathrm { z }z -test value is 1.431.431.43 for a test of the difference between two large sample means, then the null hypothesis should not be rejected.

A recent survey reported that in a sample of 300 students who attend community colleges, 105 work at least 20 hours a week. In a sample of 225 students attending universities, only 20 students were found to Work at least 20 hours per week. What is the test value?

The critical value for a two-tailed F -test is 2.65, when a=0.05a = 0.05a=0.05 , the sample size from which the variance for the numerator was obtained = 10, and the sample size from which the variance for the denominator was obtained = 15.

If the samples are dependent, the f - test for dependent samples is used.

What is the test value? Use a=0.05a = 0.05a=0.05 . (Use the variances unequal formula.)

If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

For normally distributed populations, if two samples are independent and the variances are known, the z - test is used.

A conservationist wants to know if the average water level(in meters) in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at α=0.01\alpha = 0.01α=0.01 Horseshoe Lake Swan Lake 43 38 \sigma 3.2 2.4 n 23 23

If the variances are not known, and one or both sample sizes are less than 30, the F -test must be used.

The critical value for a one-tailed right F -test is 2.57, when a=0.025a = 0.025a=0.025 , the degrees of freedom for the numerator = 15, and the degrees of freedom for the denominator = 20.

A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station Wagons is $3,900. For α=0.05\alpha = 0.05α=0.05 what is the test value?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

What is the null hypothesis? Use $\alpha = 0.05$ .

Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town and it is believed that the average hourly wages charged by both agencies are the same. Test this claim at $a=0.05$

The critical value for a two-tailed F -test is 2.65, when $a = 0.05$ , the sample size from which the variance for the numerator was obtained = 10, and the sample size from which the variance for the denominator was obtained = 15.

What is the test value? Use $a = 0.05$ . (Use the variances unequal formula.)

A conservationist wants to know if the average water level(in meters) in Horseshoe Lake is more than the average water level in Swan Lake. Test his hypothesis at $\alpha = 0.01$ Horseshoe Lake Swan Lake 43 38 \sigma 3.2 2.4 n 23 23

The critical value for a one-tailed right F -test is 2.57, when $a = 0.025$ , the degrees of freedom for the numerator = 15, and the degrees of freedom for the denominator = 20.

A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station Wagons is $3,900. For $\alpha = 0.05$ what is the test value?