Question 1
A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?
A. 3.9
B. 4.8
C. 4.9
D. 3.7
Question 2 A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test.
A. H0: µ > 170; Ha: µ = 170
B. H0: µ < 170; Ha: µ = 170
C. H0: µ = 170; Ha: µ > 170
D. H0: µ = 160; Ha: µ > 160
Question 3
A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?
A. 1.12
B. 1.48
C. 1.84
D. 2.15
Question 4
A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
A. The population is all shy workers.
B. The population cannot be identified from the description of the study.
C. The population is all American workers.
D. The population is all American professional workers (doctors, lawyers, CPA's, and the like..
Question 5
A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg. Assume that the population standard deviation is 4.9 mg.
A. Since the test statistic is greater than the critical z, there is sufficient evidence to accept the null hypothesis and to support the claim that the mean content of acetaminophen is 600 mg.
B. Since the test statistic is greater than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.
C. Since the test statistic is less than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.
D. Since the test statistic is greater than the critical z, there is insufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.
Question 6
z = 1.8 for Ha: µ > claimed value. What is the P-value for the test?
A. 0.9641
B. 3.59
C. 96.41
D. 0.0359
Question 7
= 4.8 minutes. In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that
1.2 there is sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.?A. With a z of
B. With a P-value of 0.2302 there is not sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.
C. With a P-value of 0.2302 there is sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.
D. With a z of -1.2 there is not sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.
Question 8
A right-tailed test is conducted at the 5% significance level. Which of the following z-scores is the smallest one in absolute value that leads to rejection of the null hypothesis?
A. 1.61
B. 1.85
C. -1.98
D. -2.06
Question 11
A consumer group claims that the mean running time for a certain type of flashlight battery is not the same as the manufacturer's claims. Determine the null and alternative hypotheses for the test described.
A. H0: µ = Manufacturer's claims Ha: µ < Manufacturer's claims
B. H0: µ = Manufacturer's claims Ha: µ ? Manufacturer's claims
C. H0: µ = Manufacturer's claims Ha: µ > Manufacturer's claims
D. H0: µ ? Manufacturer's claims Ha: µ = Manufacturer's claims
Question 12
A poll of 1,068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.
A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.
B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.
D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that
more than half of all voters prefer Democrat
Question 13
A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.
A. Conclusion: Support the claim that the mean is less than 9.4 minutes.
B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.
C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.
D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.
Question 14
The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
A. All games played by the team in question in which the attendance is over 4000
B. All future home games to be played by the team in question
C. All home games played by the team in question
D. None of the populations given are appropriate
Question 15
A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.
A. There is sufficient evidence to support the claim that the true proportion is less than 29 percent.
B. There is not sufficient evidence to support the claim that the true proportion is greater than 29 percent.
C. There is sufficient evidence to support the claim that the true proportion is equal to 29 percent.
D. There is sufficient evidence to support the claim that the true proportion is greater than 29 percent.
Question 17
If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?
A. 0.05
B. 0.025
C. 0.01
D. It is not significant at any of the levels given
There is not sufficient information here to answer this. Is there information missing from the question?
Question 18
In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:
H0 : µ = 8.0 hours
Ha : µ > 8.0 hours
Explain the meaning of a Type II error.
A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hours
B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ > 8.0 hours
C. Concluding that µ > 8.0 hours
D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours
Question 20
At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 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.
Formulate the null and alternative hypotheses for the study described.
A. Ho: µ = 18.4 hours H ? : µ ? 18.4 hours
B. Ho: µ = 18.4 hours H ? : µ < 18.4 hours
C. Ho: µ ? 18.4 hours H ? : µ < 18.4 hours
D. Ho: µ = 18.4 hours H ? : µ > 18.4 hours
Question 31
The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem 8 had been 3.427, state your conclusion about the relationship between gender and colorblindness.
A. Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B. Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
D. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
Question 34
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.
A. Colorblind Female 4.8; Not Colorblind Female 55.2
B. Colorblind Female 3.2; Not Colorblind Female 36.8
C. Colorbl
Question 36
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.
A. Colorblind Male 4.8; Not Colorblind Male 55.2
B. Colorblind Male 6.8; Not Colorblind Male 53.2
C. Colorblind Male 4.8; Not Colorblind Male 55.4
D. Colorblind Male 4.8; Not Colorblind Male 56.2
Question 37
A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative hypotheses for this test.
A. H0: µ > 170; Ha: µ = 170
B. H0: µ < 170; Ha: µ = 170
C. H0: µ = 170; Ha: µ > 170
D. H0: µ = 160; Ha: µ > 160
Question 27
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 8 52 60
Female 2 38 40
Total 10 90 100
Find the value of the χ2 statistic for the data above.
A. 1.463
B. 1.852
C. 1.947
D. 1.949
Question 29
Which of the following statements is true?
A. The p distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
B. The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
C. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
D. The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.
Question 30
Which of the following statements is true?
A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.
B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.
C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.
D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.
Question 31
The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem 8 had been 3.427, state your conclusion about the relationship between gender and colorblindness.
A. Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B. Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
D. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
Question 32
The following data were analyzed using one-way analysis of variance.
A B C
34 27 19
26 23 31
31 29 22
28 21 22
which one of the following statements is correct?
A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.
B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.
C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal.
D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal.
Question 33
The __________ test statistic is for the one-way analysis of variance.
A. P-Value
B. t
C. F
D. p
Question 34
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Colorblind Not Colorblind Total
Male 7 53 60
Female 1 39 40
Total 8 92 100
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.
A. Colorblind Female 4.8; Not Colorblind Female 55.2
B. Colorblind Female 3.2; Not Colorblind Female 36.8
C. Colorblind Female 4.8; Not Colorblind Female 35.2
D. Colorblind Female 3.8; Not Colorblind Female 36.2