Question 1

When we fail to reject the null hypothesis,we

Accepted Answer

A) claim that a significant difference exists between groups. 
B) have committed a Type I error. 
C) have obtained a t-value greater than our critical t-value. 
D) conclude that sampling variability is responsible for our obtained difference. 
E) have committed a Type II error. 
A) claim that a significant difference exists between groups. 
B) have committed a Type I error. 
C) have obtained a t-value greater than our critical t-value. 
D) conclude that sampling variability is responsible for our obtained difference. 
E) have committed a Type II error.

Question 2

A researcher was interested in comparing the number of hours of television watched each day by two-year-olds and three-year-olds.A random sample of 18 two-year-olds and 18 three-year-olds yielded the follow data. $$\begin{array} { r r | l r } 
&\text { 2-year-olds } & \text { 3-year-olds } \
\hline 0.5 & 1.5 & 2.0 & 3.0 \
1.5 & 2.0 & 1.5 & 1.5 \
1.5 & 0 & 1.5 & 2.0 \
1.0 & 1.0 & 1.0 & 0 \
1.0 & 0 & 0 & 1.5 \
2.0 & 1.5 & 1.5 & 2.0 \
2.5 & 2.0 & 2.5 & 2.0 \
0.5 & 0 & 3.0 & 1.0 \
1.5 & 2.5 & 1.5 & 0.5
\end{array}$$ Find a 95% confidence interval for the difference, $\mu 2$ - $\mu 3$ ,between the mean number of hours for two-year-olds and the mean number of hours for three-year-olds.

Accepted Answer

A) (-0.87,0.26) 
B) (1.25,1.56) 
C) (-0.87,-0.26) 
D) (-1.56,-1.25) 
E) (-0.26,0.87) 
A) (-0.87,0.26) 
B) (1.25,1.56) 
C) (-0.87,-0.26) 
D) (-1.56,-1.25) 
E) (-0.26,0.87)

Question 3

A researcher was interested in comparing the heights of women in two different countries.Independent random samples of 9 women from country A and 9 women from country B yielded the following heights (in centimetres). $$\begin{array} { c | c } 
\text { Country A } & \text { Country B } \
\hline 162.8 & 165.9 \
168.7 & 152.9 \
156.7 & 156.7 \
157.5 & 167.1 \
170.9 & 154.9 \
164.8 & 164.1 \
164.3 & 152.4 \
172.7 & 166.1 \
161.5 & 149.9
\end{array}$$ Determine a 90% confidence interval for the difference, $\mu _ { 1 }$ - $\mu _ { 2 }$ ,between the mean height of women in Country A and the mean height of women in Country B.

Accepted Answer

A) (0.4,10.7) 
B) (1.4,9.2) 
C) (0.8,14.2) 
D) (161.4,164.3) 
E) (0.7,4.2) 
A) (0.4,10.7) 
B) (1.4,9.2) 
C) (0.8,14.2) 
D) (161.4,164.3) 
E) (0.7,4.2)

Question 4

When testing the 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)represents a population whose mean is different from the mean for the untreated population? Explain. $$\begin{array} { | l | l | l | l | } 
\hline & \text { t-Test: Two Sample for Means } & & \
\hline 1 & & \text { Variable 1 } & \text { Variable } 2 \
\hline 2 & \text { Mean } & 65.10738 & 66.18251 \
\hline 3 & \text { Known V ariance } & 8.102938 & 10.27387 \
\hline 4 & \text { Observations } & 50 & 50 \
\hline 5 & \text { Hypothesized Mean Difference } & 0 & \
\hline 6 & \text { t } & - 1.773417 & \
\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \
\hline 8 & \text { TCritical one-tail } & 1.644853 & \
\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \
\hline 10 & \text { tCritical two-tail } & 1.959961 & \
\hline
\end{array}$$

Accepted Answer

No,the P-value for a two-tail

Question 5

130 Brand X oil filters and 93 Brand Y oil filters were tested for milligrams of residue,with the following results.Find a 95% confidence interval for $\mu_Y$ - $\mu_\mathrm { X }$ . $$\begin{array} { | c | c | c | } 
\hline & \begin{array} { c } 
\text { sample } \
\text { mean }
\end{array} & \begin{array} { c } 
\text { Sample } \
\text { standard } \
\text { deviation }
\end{array} \
\hline \text { Brand } X & \text { A } & \text { B } \
\hline \text { Brand } Y & \text { C } & \text { D } \
\hline
\end{array}$$ A = 4.3 B = 0.13 C = 5.7 D = 0.11

Accepted Answer

A) (-1.44,1.43) 
B) (-1.43,-1.37) 
C) (-1.44,-1.36) 
D) (0.97,1.83) 
E) (1.37,1.43) 
A) (-1.44,1.43) 
B) (-1.43,-1.37) 
C) (-1.44,-1.36) 
D) (0.97,1.83) 
E) (1.37,1.43)

Question 6

A study was made to determine which taxi company gave quicker service.Companies A and B were each called at 50 randomly selected times.The response times were recorded.The results are as follows.
Company A Company B
Mean response time 7.6 minutes 6.9 minutes
Standard deviation 1.4 minutes 1.7 minutes
At the 0.02 level of significance,test the claim that the two companies have different mean response times.

Accepted Answer

H0: μ1 - μ2 = 0 HA: μ1 - μ2 ≠ 0 Test sta

Question 7

A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies.If the researcher claims a significant difference between groups,when in fact none exists,

Accepted Answer

A) a Type I error is made. 
B) a Type II error is made. 
C) the research hypothesis was correctly accepted. 
D) the null hypothesis was correctly accepted. 
E) the research hypothesis was correctly rejected. 
A) a Type I error is made. 
B) a Type II error is made. 
C) the research hypothesis was correctly accepted. 
D) the null hypothesis was correctly accepted. 
E) the research hypothesis was correctly rejected.

Question 8

Two types of flares are tested for their burning times (in minutes)and sample results are given below. $\text { Brand } \mathrm { X }$ $\text { Brand } \mathrm { Y }$ n = 35 n = 40 $\overline{x}$ = 19.4 $\overline{x}$ = 15.1 s = 1.4 s = 0.8
Construct a 95% confidence interval for the difference $$\mu \mathrm { X }$$ - $\mu Y$ based on the sample data.

Accepted Answer

A) (3.5,5.1) 
B) (3.8,4.8) 
C) (3.6,5.0) 
D) (-4.7,-3.9) 
E) (3.2,5.4) 
A) (3.5,5.1) 
B) (3.8,4.8) 
C) (3.6,5.0) 
D) (-4.7,-3.9) 
E) (3.2,5.4)

Question 9

A study was conducted to determine which taxi company gives quicker service.Companies A and B were each called at 50 randomly selected times.The response times were recorded.The results were as follows.
Company A Company B
Mean response time 7.6 minutes 6.9 minutes
Standard deviation 1.4 minutes 1.7 minutes

Accepted Answer

The conditions and assumptions for infer

Question 10

You wish to construct a 95% confidence interval to compare the mean measurement for two groups.A small pilot study yields sample standard deviations of 10 and 15 for Group 1 and Group 2,respectively.If we wish to obtain a margin of error of at most 5,what sample size should we take from each group? Assume equal sample sizes.

Accepted Answer

A) 46 
B) 50 
C) 48 
D) 47 
E) 49 
A) 46 
B) 50 
C) 48 
D) 47 
E) 49

Question 11

The owner of a large apartment complex had an in-ground swimming pool installed in an effort to increase tenant satisfaction.Nine tenants were randomly selected to complete a questionnaire that assessed their level of satisfaction with the apartment complex.Their scores before and after the installation of the pool are shown.The owner wants to assess the effectiveness of the pool in increasing tenant satisfaction. $$\begin{array} { c | c c } 
\begin{array} { c } 
\text { Tenant } \
\text { Number }
\end{array} & \begin{array} { c } 
\text { Level of Satisfaction } \
\text { Before Pool }
\end{array} & \begin{array} { c } 
\text { Level of Satisfaction } \
\text { After Pool }
\end{array} \
\hline 1 & 2 & 3 \
2 & 1 & 1 \
3 & 3 & 5 \
4 & 4 & 3 \
5 & 2 & 4 \
6 & 5 & 5 \
7 & 2 & 3 \
8 & 3 & 3 \
9 & 3 & 4
\end{array}$$

Accepted Answer

The two-sample t-test cannot b

Question 12

A researcher was interested in comparing the salaries of female and male employees of a particular large company.Independent random samples of 8 female employees (sample 1)and 15 male employees (sample 2)yielded the following weekly salaries (in dollars). $$\begin{array} { r | r r } 
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$

Accepted Answer

The conditions and assumptions for infer

Question 13

A consumer advocate decided to investigate the average wait time for a table for one at two local restaurants.Eighteen customers were sent to each restaurant at the same randomly selected times and the times they waited for a table were recorded in minutes.The following sample data was obtained. $$\begin{array} { r r | l r } 
&\text { Restaurant } \mathrm { A } & \text { Restaurant } \mathrm { B } \
\hline 10 & 15 & 12 & 17 \
7 & 9 & 5 & 12 \
20 & 5 & 8 & 2 \
15 & 5 & 10 & 25 \
7 & 0 & 6 & 35 \
10 & 12 & 10 & 14 \
19 & 6 & 9 & 22 \
0 & 5 & 20 & 18 \
22 & 18 & 5 & 13
\end{array}$$ Find a 95% confidence interval for the difference, $\mu _ { \mathrm { A } }$ - $\mu \mathrm { B }$ ,between the mean wait time at Restaurant A and the mean wait time at Restaurant B.

Accepted Answer

A) (-8.3,1.86) 
B) (-1.86,8.3) 
C) (-8.3,-1.86) 
D) (-13.5,-10.28) 
E) (10.28,13.5) 
A) (-8.3,1.86) 
B) (-1.86,8.3) 
C) (-8.3,-1.86) 
D) (-13.5,-10.28) 
E) (10.28,13.5)

Question 14

The Better Cookie Company claims its chocolate chip cookies have more chips than another chocolate chip cookie.120 Better Cookies and 100 of the other type of cookie were randomly selected and the number of chips in each cookie was recorded.The results are as follows.
Better Another
Mean number of chips 7.6 6.9
Standard deviation 1.4 1.7
df = 191.
At the 2% level of significance,test the claim that the population of Better Cookies has a higher mean number of chips.

Accepted Answer

H0: μ1 - μ2 = 0 HA: μ1 - μ2 > 0 Test sta

Question 15

When testing the 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)represents a population whose mean is less than the mean for the untreated population? Explain. $$\begin{array} { | l | l | l | l | } 
\hline & \text { t-Test: Two Sample for Means } & & \
\hline 1 & & \text { Variable 1 } & \text { Variable } 2 \
\hline 2 & \text { Mean } & 65.10738 & 66.18251 \
\hline 3 & \text { Known V ariance } & 8.102938 & 10.27387 \
\hline 4 & \text { Observations } & 50 & 50 \
\hline 5 & \text { Hypothesized Mean Difference } & 0 & \
\hline 6 & \text { t } & - 1.773417 & \
\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \
\hline 8 & \text { TCritical one-tail } & 1.644853 & \
\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \
\hline 10 & \text { tCritical two-tail } & 1.959961 & \
\hline
\end{array}$$

Accepted Answer

Yes,the P-value for a one-tail test is 0

Question 16

A researcher was interested in comparing the salaries of female and male employees of a particular company.Independent random samples of 8 female employees (sample 1)and 15 male employees (sample 2)yielded the following weekly salaries (in dollars). $$\begin{array} { r | r r } 
\text { Female } & \text { Male } & \
\hline 495 & 722 & 518 \
760 & 562 & 904 \
556 & 880 & 1150 \
904 & 520 & 805 \
520 & 500 & 480 \
1005 & 1250 & 970 \
743 & 750 & 605 \
660 & 1640 &
\end{array}$$ Do the data provide sufficient evidence to conclude that the mean salary of women at this company is less than the mean salary of men at the company? Perform a $\text { t-test }$ at the 5% significance level.

Accepted Answer

H0: μ1 - μ2 = 0 HA: μ1 - μ2 < 0 Test sta

Question 17

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet.Use the sample data below to test the claim that the treatment population mean μ1 is smaller than the control population mean μ2.Test the claim using a significance level of 0.01. $\text { Treatment Group }$ $\text { Control Group }$ n1 = 85 n2 = 75 $\overline{x_1}$ = 189.1 $\overline{x_2}$ = 203.7
s1 = 38.7 s2 = 39.2
df = 155.

Accepted Answer

H0: μ1- μ2 = 0 HA: μ1 - μ2 < 0 Test stat

Question 18

A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet.Use the sample data below to test the claim that the treatment population mean μ1 is smaller than the control population mean μ2.Test the claim using a significance level of 0.01. $\text { Treatment Group }$ $\text { Control Group }$ n1 = 85 n2 = 75 $\bar { x1}$ = 189.1 $\overline{x _ { 2 }}$ = 203.7
s1 = 38.7 s2 = 39.2

Accepted Answer

H0: μ1- μ2 = 0 HA: μ1 - μ2 < 0 Test stat

Question 19

Two machines are being considered to weigh luggage at an airport.A standard 30 kg weight is used to test the machines.Sample weigh-ins were taken from each machine and the following results were obtained. $$\begin{array} { l c c } 
& \text { Machine 1 } & \text { Machine 2 } \
\hline \text { Sample size } & 25 & 36 \
\text { Sample mean } & 31.8 \mathrm {~kg} & 30.9 \mathrm {~kg} \
\text { Sample SD } & 2.2 \mathrm {~kg} & 1.98 \mathrm {~kg} \
\hline
\end{array}$$ At the 0.02 level of significance,test the claim that the population mean for Machine 1 is different from the population mean for Machine 2.

Accepted Answer

H0: μ1 - μ2 = 0 HA: μ1 - μ2 ≠ 0 Test sta

Question 20

When testing for a difference between the means of a treated population and an untreated population,the computer display below is obtained.Explain what the P-value of 0.0768 means in this context. $$\begin{array} { | l | l | l | l | } 
\hline & \text { t-Test: Two Sample for Means } & & \
\hline 1 & & \text { Variable 1 } & \text { Variable } 2 \
\hline 2 & \text { Mean } & 65.10738 & 66.18251 \
\hline 3 & \text { Known V ariance } & 8.102938 & 10.27387 \
\hline 4 & \text { Observations } & 50 & 50 \
\hline 5 & \text { Hypothesized Mean Difference } & 0 & \
\hline 6 & \text { t } & - 1.773417 & \
\hline 7 & \text { P(T<=t) one-tail } & 0.0384 & \
\hline 8 & \text { TCritical one-tail } & 1.644853 & \
\hline 9 & \text { P(T<=t) two-tail } & 0.0768 & \
\hline 10 & \text { tCritical two-tail } & 1.959961 & \
\hline
\end{array}$$

Accepted Answer

If the means for the two group

When we fail to reject the null hypothesis,we

130 Brand X oil filters and 93 Brand Y oil filters were tested for milligrams of residue,with the following results.Find a 95% confidence interval for $\mu_Y$ - $\mu_\mathrm { X }$ . sample mean Sample standard deviation Brand X A B Brand Y C D A = 4.3 B = 0.13 C = 5.7 D = 0.11

A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies.If the researcher claims a significant difference between groups,when in fact none exists,

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

Exam 21: Comparing Means

When we fail to reject the null hypothesis,we

130 Brand X oil filters and 93 Brand Y oil filters were tested for milligrams of residue,with the following results.Find a 95% confidence interval for μY\mu_YμY​ - μX\mu_\mathrm { X }μX​ . sample mean Sample standard deviation Brand X A B Brand Y C D A = 4.3 B = 0.13 C = 5.7 D = 0.11

A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies.If the researcher claims a significant difference between groups,when in fact none exists,

Stats Starts Here

Displaying and Describing Categorical Data

Displaying and Summarizing Quantitative Data

Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Understanding Randomness

Sample Surveys

Experiments and Observational Studies

From Randomness to Probability

Probability Rules

Random Variables

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

The Bootstrap

Filters

130 Brand X oil filters and 93 Brand Y oil filters were tested for milligrams of residue,with the following results.Find a 95% confidence interval for $\mu_Y$ - $\mu_\mathrm { X }$ . sample mean Sample standard deviation Brand X A B Brand Y C D A = 4.3 B = 0.13 C = 5.7 D = 0.11