Question 1

P-value for $| t |$ ? 2.13 for a sample of size 31

Accepted Answer

A) 0.1040 
B) 0.0694 
C) 0.0174 
D) 0.9793 
E) 0.0415 
A) 0.1040 
B) 0.0694 
C) 0.0174 
D) 0.9793 
E) 0.0415 E

Question 2

You are concerned about the high price of gas in your city.You want to determine if the mean price for a litre of gas has exceeded $1.40.

Accepted Answer

A) Upper-tailed 
B) Two-sided 
C) Lower-tailed 
A) Upper-tailed 
B) Two-sided 
C) Lower-tailed A

Question 3

A man on trial is accused of murder in the first degree.The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent.This situation can be modeled as a hypothesis test with the following hypotheses: H0: The defendant is not guilty.
HA: The defendant is guilty.
Explain the result of a Type II error.

Accepted Answer

A) The jury will fail to reach a decision. 
B) The jury will conclude that the defendant is guilty when in fact he is guilty. 
C) The jury will conclude that the defendant is not guilty when in fact he is not guilty. 
D) The jury will conclude that the defendant is not guilty when in fact he is guilty. 
E) The jury will conclude that the defendant is guilty when in fact he is not guilty. 
A) The jury will fail to reach a decision. 
B) The jury will conclude that the defendant is guilty when in fact he is guilty. 
C) The jury will conclude that the defendant is not guilty when in fact he is not guilty. 
D) The jury will conclude that the defendant is not guilty when in fact he is guilty. 
E) The jury will conclude that the defendant is guilty when in fact he is not guilty. D

Question 4

A one-sample t-test for the mean population score on an aptitude test is performed.The hypotheses are: H0: μ = 100
HA: μ ≠ 100
The computer test statistic,t,is positive,and the P-value for the test is found to be 0.07.What is a correct interpretation of this P-value?

Accepted Answer

A) If the null hypothesis were true,the probability of observing the test statistic would be 0.07. 
B) If the null hypothesis were true,the observed sample values would occur 7% of the time. 
C) Reject the null.At a significance level of 0.05,there is strong evidence that the mean aptitude score is different from 100. 
D) If the null hypothesis were true,the probability of observing a value of the test statistic as large or larger than that observed would be 0.07. 
E) If the null hypothesis were true,the probability of observing a value of the test statistic as extreme or more extreme than actually observed would be 0.07. 
A) If the null hypothesis were true,the probability of observing the test statistic would be 0.07. 
B) If the null hypothesis were true,the observed sample values would occur 7% of the time. 
C) Reject the null.At a significance level of 0.05,there is strong evidence that the mean aptitude score is different from 100. 
D) If the null hypothesis were true,the probability of observing a value of the test statistic as large or larger than that observed would be 0.07. 
E) If the null hypothesis were true,the probability of observing a value of the test statistic as extreme or more extreme than actually observed would be 0.07.

Question 5

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 200 fellow students,finding a mean height of 166.6 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your classmates.

Accepted Answer

A) (163.73,169.27) 
B) (164.04,169.16) 
C) (165.992,167.01) 
D) (164.02,168.98) 
E) (164.91,170.09) 
A) (163.73,169.27) 
B) (164.04,169.16) 
C) (165.992,167.01) 
D) (164.02,168.98) 
E) (164.91,170.09)

Question 6

Is the mean weight of female college students still 59.4 kg? To test this,you take a random sample of 20 students,finding a mean of 61.65 kg with a standard deviation of 6.39 kg.Use a significance level of 0.10.

Accepted Answer

A) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.1318.There is not sufficient evidence that the mean weight of female students has changed. 
B) Reject the null hypothesis of μ = 59.4 with a P-value of 0.0659.There is sufficient evidence that the mean weight of female students has changed. 
C) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.9341.There is not sufficient evidence that the mean weight of female students has changed. 
D) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.8682.There is not sufficient evidence that the mean weight of female students has changed. 
E) There is not enough information to perform the test. 
A) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.1318.There is not sufficient evidence that the mean weight of female students has changed. 
B) Reject the null hypothesis of μ = 59.4 with a P-value of 0.0659.There is sufficient evidence that the mean weight of female students has changed. 
C) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.9341.There is not sufficient evidence that the mean weight of female students has changed. 
D) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.8682.There is not sufficient evidence that the mean weight of female students has changed. 
E) There is not enough information to perform the test.

Question 7

A 99% confidence interval from a sample of size 65

Accepted Answer

A) 2.390 
B) 2.576 
C) 2.643 
D) 2.660 
E) 2.326 
A) 2.390 
B) 2.576 
C) 2.643 
D) 2.660 
E) 2.326

Question 8

The football coach at a university randomly selected ten players and timed how long each player took to perform a certain drill.The times (in minutes)were: $$\begin{array} { r r r r r } 
11.8 & 6.9 & 14.3 & 13.7 & 9.0 \
7.0 & 7.6 & 12.0 & 13.8 & 9.6
\end{array}$$ Determine a 95% confidence interval for the mean time for all players.

Accepted Answer

A) (12.57,12.67) 
B) (8.57,12.57) 
C) (8.57,12.67) 
D) (8.47,12.67) 
E) (8.47,12.57) 
A) (12.57,12.67) 
B) (8.57,12.57) 
C) (8.57,12.67) 
D) (8.47,12.67) 
E) (8.47,12.57)

Question 9

The principal of a high school randomly selected six students to take an aptitude test.Their scores were: 70.0 79.5 79.3 77.0 85.6 80.9
Determine a 90% confidence interval for the mean score for all students.

Accepted Answer

A) (74.39,82.94) 
B) (82.94,82.94) 
C) (83.04,74.39) 
D) (74.49,82.94) 
E) (82.94,83.04) 
A) (74.39,82.94) 
B) (82.94,82.94) 
C) (83.04,74.39) 
D) (74.49,82.94) 
E) (82.94,83.04)

Question 10

Suppose you have obtained a confidence interval for μ,but wish to obtain a greater degree of precision.Which of the following would result in a narrower confidence interval? 
I.Increasing the sample size while keeping the confidence level fixed
II.Decreasing the sample size while keeping the confidence level fixed
III.Increasing the confidence level while keeping the sample size fixed
IV.Decreasing the confidence level while keeping the sample size fixed

Accepted Answer

A) I,III 
B) III,IV 
C) II,III 
D) II,IV 
E) I,IV 
A) I,III 
B) III,IV 
C) II,III 
D) II,IV 
E) I,IV

Question 11

A 90% confidence interval from a sample of size 105

Accepted Answer

A) 1.660 
B) 1.658 
C) 1.665 
D) 1.645 
E) 1.984 
A) 1.660 
B) 1.658 
C) 1.665 
D) 1.645 
E) 1.984

Question 12

A manufacturer claims that the mean weight of flour in its $1 \mathrm {~kg}$ bags is $1.025 \mathrm {~kg}$ .A $\text { t-test }$ is performed to determine whether the mean weight is actually less than this.The hypotheses are H0: ? = 1.025 kg
HA: ? < 1.025 kg
The mean weight for a sample of $45 \text { bags }$ of flour was $1.011 \mathrm {~kg} .$ Suppose that the $\text { P-value }$ corresponding to this sample data is 0.001.What does the P-value tell you?

Accepted Answer

A) We should fail to reject the null.The bags contain an average of 1.025 kg. 
B) If the null hypothesis were false,the probability of observing a sample mean of 1.011 kg would be 0.001. 
C) If the mean weight of the bags were really 1.025 kg,the probability of getting a sample mean of 1.011 kg or below would be 0.001. 
D) If the null hypothesis were true,the probability of having a sample mean of 1.011 kg or above is 0.001. 
E) Not enough information is given. 
A) We should fail to reject the null.The bags contain an average of 1.025 kg. 
B) If the null hypothesis were false,the probability of observing a sample mean of 1.011 kg would be 0.001. 
C) If the mean weight of the bags were really 1.025 kg,the probability of getting a sample mean of 1.011 kg or below would be 0.001. 
D) If the null hypothesis were true,the probability of having a sample mean of 1.011 kg or above is 0.001. 
E) Not enough information is given.

Question 13

You want to determine if the average gas price in your city has exceeded $1.30 per litre for regular unleaded gasoline.You take a random sample of prices from 8 gas stations ,recording the following prices: $1.33,$1.30,$1.05,$1.29,$1.37,$1.32,$1.30,$1.31.Have the conditions and assumptions for inference been met?

Accepted Answer

A) No,the Nearly Normal Condition is not met. 
B) No,the sample is not random. 
C) No,the sample is not representative. 
D) Yes,all conditions and assumptions have been met. 
E) No,the sample is more than 10% of the population. 
A) No,the Nearly Normal Condition is not met. 
B) No,the sample is not random. 
C) No,the sample is not representative. 
D) Yes,all conditions and assumptions have been met. 
E) No,the sample is more than 10% of the population.

Question 14

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 237 milligrams with s = 14.0 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Accepted Answer

A) (229.7,244.3) 
B) (228.0,246.0) 
C) (228.1,245.9) 
D) (228.1,246.0) 
E) (228.0,244.3) 
A) (229.7,244.3) 
B) (228.0,246.0) 
C) (228.1,245.9) 
D) (228.1,246.0) 
E) (228.0,244.3)

Question 15

In 2009,the average final exam score for students in an introductory math course was 72%.Five years later,a teacher wants to perform a hypothesis test to determine whether the average score of students the course has changed from the 2009 mean of 72%.The hypotheses are: H0: μ = 72%
HA: μ ≠ 72%
Explain the result of a Type I error.

Accepted Answer

A) The teacher will conclude that the average final exam score in the course has decreased when in fact it is the same. 
B) The teacher will conclude that the average final exam score in the course has increased when in fact it is the same. 
C) The teacher will conclude that the average final exam score in the course is the same when in fact it is the same. 
D) The teacher will conclude that the average final exam score in the course is different when in fact it is the same. 
E) The teacher will conclude that the average final exam score in the course is the same when in fact it is different. 
A) The teacher will conclude that the average final exam score in the course has decreased when in fact it is the same. 
B) The teacher will conclude that the average final exam score in the course has increased when in fact it is the same. 
C) The teacher will conclude that the average final exam score in the course is the same when in fact it is the same. 
D) The teacher will conclude that the average final exam score in the course is different when in fact it is the same. 
E) The teacher will conclude that the average final exam score in the course is the same when in fact it is different.

Question 16

At one school,the average amount of time that $\text { tenth-graders }$ spend watching television each week is $21.6 \text { hours. }$ The principal introduces a campaign to encourage the students to watch less television.One year later,the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of $21.6 \text { hours. }$

Accepted Answer

A) Upper-tailed 
B) Two-sided 
C) Lower-tailed 
A) Upper-tailed 
B) Two-sided 
C) Lower-tailed

Question 17

An independent laboratory tests 100 light bulbs,finding that the mean life is 103 hours with a standard deviation of 11 hours.Decide whether or not the conditions and assumptions for inference with a t-test are satisfied.Explain your answer.

Accepted Answer

The data are assumed to be a random samp

Question 18

A group of researchers wants to determine the mean annual household income for families receiving services at a large community centre.They randomly select ten families and record the following household incomes: $43,955,$42,740,$42,660,$43,800,$43,500,$44,250,$44,340,$40,390,$44,150,$44,200.Decide whether or not the conditions and assumptions for inference with a t-test are satisfied.Explain your answer.

Accepted Answer

The sample is randomly selected,and it i

Question 19

How much fat do reduced fat cookies typically have? You take a random sample of 50 reduced-fat cookies and test them in a lab,finding a mean fat content of 3.2 grams and a standard deviation of 1.1 grams of fat.Have the conditions and assumptions for inference been met?

Accepted Answer

A) No,the sample is not likely to be representative. 
B) No,we have sampled more than 10% of the population. 
C) No,the sample is not big enough to satisfy the Nearly Normal Condition. 
D) Yes,all conditions and assumptions are reasonably assumed to be met. 
E) No,it is not a random sample. 
A) No,the sample is not likely to be representative. 
B) No,we have sampled more than 10% of the population. 
C) No,the sample is not big enough to satisfy the Nearly Normal Condition. 
D) Yes,all conditions and assumptions are reasonably assumed to be met. 
E) No,it is not a random sample.

Question 20

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

Accepted Answer

A) You are 95% confident that the mean fat in reduced fat cookies is between 3.4 and 5 grams of fat. 
B) We are 95% confident that the mean fat in all cookies is between 3.4 and 5 grams. 
C) 95% of the cookies in the sample had between 3.4 and 5 grams of fat. 
D) We are 95% sure that the average amount of fat in the cookies in this study was between 3.4 and 5 grams. 
E) 95% of reduced fat cookies have between 3.4 and 5 grams of fat. 
A) You are 95% confident that the mean fat in reduced fat cookies is between 3.4 and 5 grams of fat. 
B) We are 95% confident that the mean fat in all cookies is between 3.4 and 5 grams. 
C) 95% of the cookies in the sample had between 3.4 and 5 grams of fat. 
D) We are 95% sure that the average amount of fat in the cookies in this study was between 3.4 and 5 grams. 
E) 95% of reduced fat cookies have between 3.4 and 5 grams of fat.

Exam 20: Inferences About Means

P-value for ∣t∣| t |∣t∣ ? 2.13 for a sample of size 31

You are concerned about the high price of gas in your city.You want to determine if the mean price for a litre of gas has exceeded $1.40.

A one-sample t-test for the mean population score on an aptitude test is performed.The hypotheses are: H0: μ = 100 HA: μ ≠ 100 The computer test statistic,t,is positive,and the P-value for the test is found to be 0.07.What is a correct interpretation of this P-value?

How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 200 fellow students,finding a mean height of 166.6 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your classmates.

Is the mean weight of female college students still 59.4 kg? To test this,you take a random sample of 20 students,finding a mean of 61.65 kg with a standard deviation of 6.39 kg.Use a significance level of 0.10.

A 99% confidence interval from a sample of size 65

The football coach at a university randomly selected ten players and timed how long each player took to perform a certain drill.The times (in minutes)were: 11.8 6.9 14.3 13.7 9.0 7.0 7.6 12.0 13.8 9.6 Determine a 95% confidence interval for the mean time for all players.

The principal of a high school randomly selected six students to take an aptitude test.Their scores were: 70.0 79.5 79.3 77.0 85.6 80.9 Determine a 90% confidence interval for the mean score for all students.

A 90% confidence interval from a sample of size 105

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 237 milligrams with s = 14.0 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

An independent laboratory tests 100 light bulbs,finding that the mean life is 103 hours with a standard deviation of 11 hours.Decide whether or not the conditions and assumptions for inference with a t-test are satisfied.Explain your answer.

How much fat do reduced fat cookies typically have? You take a random sample of 50 reduced-fat cookies and test them in a lab,finding a mean fat content of 3.2 grams and a standard deviation of 1.1 grams of fat.Have the conditions and assumptions for inference been met?

How much fat do reduced fat cookies typically have? You take a random sample of 51 reduced-fat cookies and test them in a lab,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

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P-value for $| t |$ ? 2.13 for a sample of size 31