Question 1

Find the appropriate p-value to test the null hypothesis, HS1U1B10S1U1B0: pS1U1B11S1U1B0 = pS1U1B12S1U1B0, using a significance level of 0.05.
-$$\begin{array} { l l } 
n _ { 1 } = 50 & n _ { 2 } = 50 \
x _ { 1 } = 3 & x _ { 2 } = 7
\end{array}$$

Accepted Answer

A) .1201 
B) .0072 
C) .1836 
D) .0613 
A) .1201 
B) .0072 
C) .1836 
D) .0613

Question 2

Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
-A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. $\begin{array}{lllllllllllllll}
\text { Before } & 70 & 80 & 92 & 99 & 93 & 97 & 76 & 63 & 68 & 71 & 74 \
\hline \text { After } & 69 & 79 & 90 & 96 & 91 & 95 & 75 & 64 & 62 & 64 & 76
\end{array}$

Accepted Answer

A)  $1.2 < \mu _ { \mathrm { d } } < 2.8$ 
B)  $- 0.2 < \mu _ { \mathrm { d } } < 4.2$ 
C)  $- 0.1 < \mu _ { \mathrm { d } } < 4.1$ 
D)  $- 0.5 < \mu _ { \mathrm { d } } < 4.5$ 
A)  $1.2 < \mu _ { \mathrm { d } } < 2.8$ 
B)  $- 0.2 < \mu _ { \mathrm { d } } < 4.2$ 
C)  $- 0.1 < \mu _ { \mathrm { d } } < 4.1$ 
D)  $- 0.5 < \mu _ { \mathrm { d } } < 4.5$

Question 3

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is $\mu _ { \mathrm { d } } = 0$. Compute the value of the $t$ test statistic.
-The differences between two sets of dependent data are 0.11, 0.21, 0.15, 0.12, 0.14. Round to the nearest hundredth.

Accepted Answer

A) 0.06 
B) 0.02 
C) 0.12 
D) 0.04 
A) 0.06 
B) 0.02 
C) 0.12 
D) 0.04

Question 4

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected.
-Independent samples from two different populations yield the following data. $\overline { x _ { 1 } } = 383 , \overline { x _ { 2 } } = 448$, s1 $= 44$, s2 $= 18$. The sample size is 177 for both samples. Find the 85 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$.

Accepted Answer

A)  $- 72 < \mu _ { 1 } - \mu _ { 2 } < - 58$ 
B)  $- 66 < \mu _ { 1 } - \mu _ { 2 } < - 64$ 
C)  $- 79 < \mu _ { 1 } - \mu _ { 2 } < - 51$ 
D)  $- 71 < \mu _ { 1 } - \mu _ { 2 } < - 59$ 
A)  $- 72 < \mu _ { 1 } - \mu _ { 2 } < - 58$ 
B)  $- 66 < \mu _ { 1 } - \mu _ { 2 } < - 64$ 
C)  $- 79 < \mu _ { 1 } - \mu _ { 2 } < - 51$ 
D)  $- 71 < \mu _ { 1 } - \mu _ { 2 } < - 59$

Question 5

Determine whether the samples are independent or consist of matched pairs.
-The accuracy of verbal responses is tested in an experiment in which individuals report their heights and then are measured. The data consist of the reported height and measured height for each individual.

Accepted Answer

A) Independent samples 
B) Matched pairs 
A) Independent samples 
B) Matched pairs

Question 6

Compute the test statistic used to test the null hypothesis that pS1U1B11 S1U1B0= pS1U1B12S1U1B0
-$$\begin{array} { l l } 
n _ { 1 } = 187 & n _ { 2 } = 177 \
x _ { 1 } = 67 & x _ { 2 } = 62
\end{array}$$

Accepted Answer

A) 4.086 
B) 0.159 
C) 2.200 
D) 0.364 
A) 4.086 
B) 0.159 
C) 2.200 
D) 0.364

Question 7

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis
-Suppose you wish to test the claim that $\mu _ { \mathrm { d } },$ , the mean value of the differences d for a population of paired data, is different from 0. Given a sample of n = 23 and a significance level of $\alpha =$ 0.05, what criterion would be used for rejecting the null hypothesis?

Accepted Answer

A) Reject null hypothesis if test statistic $> 1.717$. B) Reject null hypothesis if test statistic $> 2.074$ or $ 2.069$ or $ 1.717$ or $< - 1.717$. A) Reject null hypothesis if test statistic $> 1.717$. B) Reject null hypothesis if test statistic $> 2.074$ or $ 2.069$ or $ 1.717$ or $< - 1.717$.

Question 8

Find the appropriate p-value to test the null hypothesis, HS1U1B10S1U1B0: pS1U1B11S1U1B0 = pS1U1B12S1U1B0, using a significance level of 0.05.
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 100 & \mathrm { n } _ { 2 } = 140 \
\mathrm { x } _ { 1 } = 41 & \mathrm { x } _ { 2 } = 35
\end{array}$$

Accepted Answer

A) .0512 
B) .0086 
C) .0021 
D) .4211 
A) .0512 
B) .0086 
C) .0021 
D) .4211

Question 9

From the sample statistics, find the value of$\bar{ p}$ used to test the hypothesis that the population proportions are equal
-Among 1450 randomly selected car drivers in one city, 7.52% said that they had been involved in an accident during the past year.

Accepted Answer

A) 110 
B) 108 
C) 109 
D) 107 
A) 110 
B) 108 
C) 109 
D) 107

Question 10

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
-A coach uses a new technique in training middle distance runners. The times for 8 different athletes to run 800 meters before and after this training are shown below. $\begin{array} { c | c c c c c c c c } 
\text{Athlete} & A&B&C&D&E&F&G&H\
\hline\text{ Time before} &116&115.9&118.6&109.7&111.5&113&119&116 \
\text{training (seconds)}\
\hline\text{ Time AFTER} &116.6&114.6&116.2&110.5&109.7&113.1&115.4&112.1\
\text{training (seconds)}\
\end{array}$
Using a $0.05$ level of significance, test the claim that the training helps to improve the athletes' times for the $800 \mathrm { n }$

Accepted Answer

Test statistic t = 2

Question 11

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
-A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. $\begin{array} { l l l l l l l l l l l } \text { Before } & 74 & 83 & 75 & 88&84 & 63 & 93 & 84 & 91 & 77 \ \hline \text {After }& 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75 \end{array}$

Accepted Answer

The answer of Use the traditional method of hypothesis testing...

Question 12

Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
-If $\mathrm { d } = 3.125 , \mathrm {~S} _ { \mathrm { d } } = 2.911$, and $\mathrm { n } = 8$, determine a 99 percent confidence interval for $\mu _ { \mathrm { d } }$.

Accepted Answer

A)  $- 0.476 < \mu _ { \mathrm { d } } < 6.726$ 
B)  $1.851 < \mu _ { \mathrm { d } } < 6.726$ 
C)  $1.851 < \mu _ { \mathrm { d } } < 4.399$ 
D)  $- 0.476 < \mu _ { \mathrm { d } } < 4.399$ 
A)  $- 0.476 < \mu _ { \mathrm { d } } < 6.726$ 
B)  $1.851 < \mu _ { \mathrm { d } } < 6.726$ 
C)  $1.851 < \mu _ { \mathrm { d } } < 4.399$ 
D)  $- 0.476 < \mu _ { \mathrm { d } } < 4.399$

Question 13

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth.
-$$\begin{array} { l | l l l l l l l } 
\mathrm { X } & 227 & 189 & 220 & 182 & 246 & 277 & 302 \
\hline \mathrm { Y } & 217 & 154 & 195 & 153 & 227 & 246 & 284
\end{array}$$

Accepted Answer

A) 143.4 
B) 23.9 
C) 14.3 
D) 31.1 
A) 143.4 
B) 23.9 
C) 14.3 
D) 31.1

Question 14

Solve the problem.
-A researcher wished to perform a hypothesis test to test the claim that the rate of defectives among the computers of two different manufacturers are the same. She selects two independent random samples and obtains the following sample data. Manufacturer 
A: $\mathrm { n } _ { 1 } = 400$, rate of defectives: $1.5 \%$Manufacturer 
B: $\mathrm { n } _ { 2 } = 200$, rate of defectives: $3.5 \%$
 Can the methods of this section be used to perform a hypothesis test to test for the equality of the two population proportions? Go through the steps of checking whether the conditions for the hypothesis test for two population proportions are satisfied. Show your calculations and state your conclusion.

Accepted Answer

\[\begin{array} { l } 
\mathrm { x } _ {

Question 15

Determine whether the samples are independent or consist of matched pairs.
-The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

Accepted Answer

A) Matched pairs 
B) Independent samples 
A) Matched pairs 
B) Independent samples

Question 16

Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.
-A coach uses a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before and after this training are shown below. $\begin{array} { c | c c c c c c c c } 
\text{Athlete} & A&B&C&D&E&F&G&H&I\
\hline\text{ Time before} &115.2&120.9&108.0&112.4&107.5&119.1&121.3&110.8&122.3 \
\text{training (seconds)}\
\hline\text{ Time AFTER} &116.0&119.1&105.1&111.9&109.1&115.2&118.5&110.7&120.9\
\text{training (seconds)}\
\end{array}$
Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" times.

Accepted Answer

A)  $- 0.85 < \mu _ { \mathrm { d } } < 3.29$ 
B)  $- 0.76 < \mu _ { \mathrm { d } } < 3.20$ 
C)  $- 0.82 < \mu _ { \mathrm { d } } < 3.26$ 
D)  $- 0.54 < \mu _ { \text {d } } < 2.98$ 
A)  $- 0.85 < \mu _ { \mathrm { d } } < 3.29$ 
B)  $- 0.76 < \mu _ { \mathrm { d } } < 3.20$ 
C)  $- 0.82 < \mu _ { \mathrm { d } } < 3.26$ 
D)  $- 0.54 < \mu _ { \text {d } } < 2.98$

Question 17

Use the computer display to solve the problem.
-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is different from the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } 
\hline & \text { t-Test: Two Sample for Means } & & \
\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \
\hline 2 & \text { Mean } & 65.10738 & 66.18251 \
\hline 3 & \text { Known Variance } & 8.102938 & 10.27387 \
\hline 4 & \text { Observations } & 50 & 50 \
\hline 5 & \text { Hypothesized Mean Difference } & 0 & \
\hline 6 & \text { t } & - 1.773417 & \
\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \
\hline 8 & \text { TCritical one-tail } & 1.644853 & \
\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \
\hline 10 & \text { tCritical two-tail } & 1.959961 & \
\hline
\end{array}$$

Accepted Answer

No, the P-value for a two-tail

Question 18

Compute the test statistic used to test the null hypothesis that pS1U1B11 S1U1B0= pS1U1B12S1U1B0
-$$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 719 & \mathrm { n } _ { 2 } = 3852 \
\mathrm { x } _ { 1 } = 101 & \mathrm { x } _ { 2 } = 612
\end{array}$$

Accepted Answer

A) 0.125 
B) 0.395 
C) 0.312 
D) 0.156 
A) 0.125 
B) 0.395 
C) 0.312 
D) 0.156

Question 19

Use the computer display to solve the problem.
-When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.01 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1)comes from a population with a mean that is greater than the mean for the placebo population? Explain. $$\begin{array} { | l | l | l | l | } 
\hline & \text { t-Test: Two Sample for Means } & & \
\hline 1 & & \text { Variable 1 } & \text { Variable 2 } \
\hline 2 & \text { Mean } & 171.6392 & 168.7718 \
\hline 3 & \text { Known Variance } & 47.51672 & 41.08293 \
\hline 4 & \text { Observations } & 50 & 50 \
\hline 5 & \text { Hypothesized Mean Difference } & 0 & \
\hline 6 & \text { t } & 2.154057 & \
\hline 7 & \text { P(T>=t) one-tail } & 0.0158 & \
\hline 8 & \text { TCritical one-tail } & 1.644853 & \
\hline 9 & \text { P(T>=t) two-tail } & 0.0316 & \
\hline 10 & \text { tCritical two-tail } & 1.959961 & \
\hline
\end{array}$$

Accepted Answer

No, the P-value for a one-tail test is 0

Question 20

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that
two dependent samples have been randomly selected from normally distributed populations.
-The table below shows the weights of seven subjects before and after following a particular diet for two months. $$\begin{array}{l}
\begin{array} { c | r r r r r r r } 
\text { Subject } & A & B & C & D & E & F & G \
\hline \text { Before } & 157 & 160 & 156 & 183 & 190 & 157 & 161 \
\hline \text { After } & 150 & 151 & 154 & 188&176 & 159 & 149
\end{array}\
\text { Using a } 0.01 \text { level of significance, test the claim that the diet is effective in reducing weight. }
\end{array}$$

Accepted Answer

Test statistic t = 1

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05. - =50 =50 =3 =7

Determine whether the samples are independent or consist of matched pairs. -The accuracy of verbal responses is tested in an experiment in which individuals report their heights and then are measured. The data consist of the reported height and measured height for each individual.

Compute the test statistic used to test the null hypothesis that p₁= p₂ - =187 =177 =67 =62

Find the appropriate p-value to test the null hypothesis, H₀: p₁ = p₂, using a significance level of 0.05. - =100 =140 =41 =35

From the sample statistics, find the value of $\bar{ p}$ used to test the hypothesis that the population proportions are equal -Among 1450 randomly selected car drivers in one city, 7.52% said that they had been involved in an accident during the past year.

The two data sets are dependent. Find $\bar { d }$ to the nearest tenth. - 227 189 220 182 246 277 302 217 154 195 153 227 246 284

Determine whether the samples are independent or consist of matched pairs. -The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

Compute the test statistic used to test the null hypothesis that p₁= p₂ - =719 =3852 =101 =612

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 9: Inferences From Two Samples

Find the appropriate p-value to test the null hypothesis, H0: p1 = p2, using a significance level of 0.05. - =50 =50 =3 =7