Question 1

$$\text { In comparing the two variances below, what is the test value and what are the degrees of freedom that }$$
$\begin{array}{|l|c|c|}
\hline & \text { Variance } & \text { Number of values } \
\hline \text { Sample 1 } & 5 & 19 \
\hline \text { Sample 2 } & 11 & 29 \
\hline
\end{array}$

Accepted Answer

A)  test value = 0.45, degrees of freedom = 19 and 29 
B)  test value = 0.45, degrees of freedom = 18 and 28 
C)  test value = 2.20, degrees of freedom = 28 and 18 
D)  test value = 2.20, degrees of freedom = 29 and 19

Question 2

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of
freedom = 7 and $a = 0.025$

Accepted Answer

The answer of The critical value for a left-tailed t-test...

Question 3

An educational researcher is analyzing the test scores for statistics students taught using two different methods - a traditional method and a web-based, self-paced method. Can he conclude, at $\ddagger = .05$, that the test scores in the web-based, self-paced method are lower?
$\begin{array}{|l|c|c|}
\hline & \text { Traditional } & \text { Web-based Self-paced } \
\hline \text { Sample size } & 80 & 60 \
\hline \text { Mean test score } & 86 & 84 \
\hline \text { Sample variance } & 24 & 46 \
\hline
\end{array}$

Accepted Answer

A)  The data do not support the claim because the test value 0.94 is less than 1.64. 
B)  The data do not support the claim because the test value 0.94 is less than 1.96. 
C)  The data support the claim because the test value 1.94 is less than 1.96. 
D)  The data support the claim because the test value 1.94 is greater than 1.65.

Question 4

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 hypothesis would be 
$\begin{array}{|l|l|l|}
\hline & \text { Crag Lake } & \text { Gull Lake } \
\hline \bar{r} & 44 & 33 \
\hline 8 & 3.9 & 2.4 \
\hline \| & 22 & 21 \
\hline
\end{array}$
 ________________________________________

Accepted Answer

The answer of A conservationist wants to know if the...

Question 5

A marketing firm asked a random set of married and single men how much they were willing to spend for a vacation. At ${ } ^ { \star } = .05$, is a difference in the two amounts?
$\begin{array}{|l|c|c|}
\hline & \text { Married men } & \text { Single men } \
\hline \text { Sample size } & 80 & 60 \
\hline \text { Mean spending } & 380 & 325 \
\hline \text { Sample variance } & 6000 & 8000 \
\hline
\end{array}$

Accepted Answer

A)  No, because the test value 0.26 is inside the interval (-1.96, 1.96) 
B)  Yes, because the test value 3.81 is outside the interval (-1.96, 1.96) 
C)  Yes, because the test value 1.33 is inside the interval (-1.96, 1.96) 
D)  No, because the test value 1.33 is outside the interval (-1.96, 1.96)

Question 6

Samples are independent when they are not related.

Accepted Answer

A) True 
 B)False

Question 7

A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at ${ } ^ { \pm } = .10$, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?
$\begin{array}{|l|c|c|}
\hline & \text { Pine trees } & \text { Spruce trees } \
\hline \text { Sample size } & 80 & 60 \
\hline \text { Mean trunk diameter }(\mathrm{cm}) & 35 & 33 \
\hline \text { Sample variance } & 130 & 150 \
\hline
\end{array}$

Accepted Answer

A)  The data do not support the claim because the test value 0.48 is less than 1.28. 
B)  The data do not support the claim because the test value 0.98 is less than 1.28. 
C)  The data do not support the claim because the test value 0.98 is less than 1.64. 
D)  The data do not support the claim because the test value 0.48 is less than 1.64.

Question 8

A study on the oxygen consumption rate (OCR) of sea cucumbers involved a random sample of size 10 at 15oC and a second random sample of size 7 kept at 18oC. If one tested the hypothesis that this range
Of temperature had no effect on the OCR, the degrees of freedom for the test statistic would be (assume
Equal variability)

Accepted Answer

A)  9 
B)  10 
C)  15 
D)  16

Question 9

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? $$\begin{array} { | l | c | c | } 
\hline & \text { Standard Deviation } & \text { Number of values } \
\hline \text { Sample 1 } & 7 & 17 \
\hline \text { Sample 2 } & 2 & 25 \
\hline
\end{array}$$

Accepted Answer

A)  test value = 3.50, degrees of freedom = 17 and 25 
B)  test value = 3.50, degrees of freedom = 16 and 24 
C)  test value = 12.25, degrees of freedom = 17 and 25 
D)  test value = 12.25, degrees of freedom = 16 and 24

Question 10

$$\begin{array}{l}
\text { In testing the equality of the two means below, what is the test statistic? (Use the unequal variances }\
\begin{array} { | l | c | c | } 
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample size } & 8 & 13 \
\hline \text { Sample mean } & 80 & 115 \
\hline \text { Sample variance } & 450 & 100 \
\hline
\end{array}
\end{array}$$

Accepted Answer

A)  -2.36 
B)  -0.22 
C)  -0.55 
D)  -4.38

Question 11

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18

Accepted Answer

A)  -1.65 
B)  -2.33 
C)  -2.58 
D)  -1.96

Question 12

$$\begin{array}{l}
\text { In testing the equality of the two means below, what is the test statistic? (Use the equal variances }\
\begin{array} { | l | c | c | } 
\hline & \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample size } & 12 & 9 \
\hline \text { Sample mean } & 115 & 80 \
\hline \text { Sample variance } & 700 & 400 \
\hline
\end{array}
\end{array}$$

Accepted Answer

A)  3.31 
B)  1.75 
C)  0.31 
D)  2.31

Question 13

One of the requirements for the z - test for comparing two proportions is that the samples must be
dependent on each other.

Accepted Answer

A) True 
 B)False

Question 14

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.
 $$\begin{array} { | l | l | } 
\hline \text { Miles / Gal Without } & \text { Miles / Gal With } \
\hline 21.2 & 23.8 \
\hline 25.4 & 25.6 \
\hline 20.9 & 22.4 \
\hline 27.6 & 28.3 \
\hline 22.8 & 24.5 \
\hline 27.3 & 28.8 \
\hline 23.4 & 25.2 \
\hline
\end{array}$$
-State the alternative hypothesis.

Accepted Answer

A)  $H _ { 1 } : \mu _ { D } = 0$ 
B)  $H _ { 1 } : \mu _ { D } > 0$ 
C)  $H _ { 1 } , \mu _ { D } < 0$ 
D)  $H _ { 1 } = \mu _ { D } = 0$

Question 15

A local charity thinks that people in River Heights give more money to their charity than people in Lakeview. They conducted a survey of 24 people in each subdivision and recorded the results. Is their $\text { hypothesis correct? Let } \alpha=0.01 \text {. }$

Accepted Answer

The answer of A local charity thinks that people in...

Question 16

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.
 $$\begin{array} { | l | l | } 
\hline \text { Miles / Gal Without } & \text { Miles / Gal With } \
\hline 21.2 & 23.8 \
\hline 25.4 & 25.6 \
\hline 20.9 & 22.4 \
\hline 27.6 & 28.3 \
\hline 22.8 & 24.5 \
\hline 27.3 & 28.8 \
\hline 23.4 & 25.2 \
\hline
\end{array}$$
-Determine the mean of the difference.

Accepted Answer

A)  -0.96 
B)  -6.3 
C)  1.43 
D)  -1.43

Question 17

A bond analyst is analyzing the interest rates for equivalent provincial bonds and Canada bonds. At $\ddagger = .05$, is there a difference in the interest rates paid?
$\begin{array}{|l|c|c|}
\hline & \text { Canada bonds } & \text { Provincial bonds } \
\hline \text { Sample size } & 80 & 40 \
\hline \text { Mean interest rate }(\%) & 3.9 & 4.15 \
\hline \text { Sample variance } & 0.01 & 0.03 \
\hline
\end{array}$

Accepted Answer

A)  Yes, because the test value -8.45 is outside the interval (-1.96, 1.96) 
B)  Yes, because the test value -2.86 is outside the interval (-1.96, 1.96) 
C)  Yes, because the test value 71.43 is outside the interval (-1.96, 1.96) 
D)  No, because the test value -0.03 is inside the interval (-1.96, 1.96)

Question 18

When comparing two variances or standard deviations, a f -test is used.

Accepted Answer

A) True 
 B)False

Question 19

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured), how many degrees of freedom
Should the researcher use in her t-test critical value?

Accepted Answer

A)  8 
B)  9 
C)  16 
D)  17

Question 20

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the
Variance of 12 business lunches was $0.87. What is the test value?

Accepted Answer

A)  3.1 
B)  9.61 
C)  49.5 
D)  7.03

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

$\text { In comparing the two variances below, what is the test value and what are the degrees of freedom that }$ $\begin{array}{|l|c|c|}\hline & \text { Variance } & \text { Number of values } \\\hline \text { Sample 1 } & 5 & 19 \\\hline \text { Sample 2 } & 11 & 29 \\\hline\end{array}$

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and $a = 0.025$

Samples are independent when they are not related.

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18

One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other.

When comparing two variances or standard deviations, a f -test is used.

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured) , how many degrees of freedom Should the researcher use in her t-test critical value?

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the Variance of 12 business lunches was $0.87. What is the test value?

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

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and a=0.025a = 0.025a=0.025

Samples are independent when they are not related.

Calculate the critical value. Use a=0.05a = 0.05a=0.05 Refer To: 09-18

One of the requirements for the z - test for comparing two proportions is that the samples must be dependent on each other.

When comparing two variances or standard deviations, a f -test is used.

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured) , how many degrees of freedom Should the researcher use in her t-test critical value?

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the Variance of 12 business lunches was $0.87. What is the test value?

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of freedom = 7 and $a = 0.025$

Calculate the critical value. Use $a = 0.05$ Refer To: 09-18