Multiple choice questions:
Question 1
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
Question 2
The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by s = $13,700. 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 current seventh graders at the principal's school
B. Seventh graders' families at the school with a standard deviation of $13,700
C. All of the families of the class of seventh graders at the principal's school
D. All seventh graders' families
Question 3
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 Democrats.
Question 4
without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.
A.is less than 1 standard deviation above the claimed mean.
B.is more than 4 standard deviations above the claimed mean.
C.is less than 1 standard deviation above the claimed mean.
D.is more than 4 standard deviations above the claimed mean.
Question 5
In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 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 9.3 minutes. Formulate the null and alternative hypotheses for the study described.
A. Ho: µ = 9.3 minutes H a : µ < 9.3 minutes
B.Ho: µ = 9.3 minutes H a : µ > 9.3 minutes
C.Ho: µ = 9.3 minutes H a : µ ¹ 9.3 minutes
D.Ho: µ ¹ 9.3 minutes H a : µ = 9.3 minutes
Question 6
A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.
Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
B .Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
C. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
D.Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
Question 7
In the past, the mean running time for a certain type of flashlight battery has been 9.8 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 = 9.8 hours
Ha : µ > 9.8 hours
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.
A. Type I error
B. Type II error
C. Correct decision
D. Can not be determined from this information
Question 8
A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.
A. Conclusion: Support the claim that the mean is equal to 16 ounces.
B. Conclusion: Support the claim that the mean is greater than 16 ounces.
C. Conclusion: Support the claim that the mean is not equal to 16 ounces.
D. Conclusion: Support the claim that the mean is less than 16 ounces.
Question 9
A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?
A. 97.5%
B. 5%
C. 2.5%
D. 95%
Question 10
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 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 ¹ Manufacturer's claims
C.H0: µ = Manufacturer's claims Ha: µ > Manufacturer's claims
D.H0: µ ¹ Manufacturer's claims Ha: µ = Manufacturer's claims
Question 12
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 13
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 14
A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective.
A. Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.
B. Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
C. Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.
D. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective.
Question 15
A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?
A. Greater than or equal to .010
B. Greater than or equal to 0.05
C. Less than or equal to 0.10
D. Less than or equal to 0.05
Question 16
A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
A. Greater than or equal to 0.10
B. Less than or equal to 0.05
C. Less than or equal to 0.10
D. Greater than or equal to 0.05
Question 17
A study of a brand of "in the shell peanuts" gives the following results:
A significant event at the 0.01 level is a fan getting a bag with how many peanuts?
A. 30 peanuts
B. 25 or 30 peanuts
C. 25 or 55 peanuts
D. 25 peanuts
Question 18
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 s = 4.8 minutes.
A. With a z of -1.2 there is sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.
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 19
A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.
A. The z of - 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
B. The z of - 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
C. The z of - 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
D. The z of - 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.
Question 20
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 21
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
State the null and alternative hypothesis for the test associated with this data.
A. H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are not related in any way.
B. H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are related in some way.
C. H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are not related in any way.
D. H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.
Question 22
A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?
A. 4.4
B. 4.6
C. 4.8
D. 5.0
Question 23
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 24
The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?
A. Smaller. E increases as the square root of the sample size gets larger.
B. Smaller. E decreases as the square root of the sample size gets larger.
C. Larger. E decreases as the square root of the sample size gets larger.
D. Larger. E increases as the square root of the sample size gets larger.
Question 25
A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x¯ is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.
A. df = 7; E = 3.3445.38 = 5.6566
B. df = 8; E = 3.3445.38 = 5.6566
C. df = 6; E = 2.3656.38 = 5.769
D. df = 7; E = 2.3656.38 = 5.869
Question 26
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 27
A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed.
Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer's requirements. Use the partial t-table below.
Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.
B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.
C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.
D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.
Question 28
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.
Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer's requirements. Use the partial t-table below.
Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.
C. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.
D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.
Question 29
A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?
A. 4.6
B. 4.4
C. 4.2
D. 5.6
Question 30
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.
Do not reject H0.
Reject H0.
There is sufficient evidence to support the claim that gender and colorblindness are not related.
D. There is not sufficient evidence to accept or reject H0.
Question 31
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
Question 32
Which of the following statements is true?
The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
B. The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.
C. The t distribution cannot be used when finding a confidence interval for the population mean whenever the sample size is small.
D. The p distribution cannot be used when finding a confidence interval for the sample mean whenever the sample size is small.
Question 33
A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed. State the null and alternative hypotheses for this test.
A. H0: µ = 160; Ha: µ > 150
B.H0: µ = 150; Ha: µ > 150
C.H0: µ = 160; Ha: µ > 160
D. H0: µ = 140; Ha: µ > 160
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
|
8
|
52
|
60
|
|
Female
|
2
|
38
|
40
|
|
Total
|
10
|
90
|
100
|
If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.
|
Colorblind
|
Not Colorblind
|
Total
|
|
Male
|
|
|
|
|
Female
|
|
|
|
|
Total
|
|
|
|
A. Male Colorblind 6.0; Male Not Colorblind 54.0
B. Male Colorblind 7.0; Male Not Colorblind 53.0
C. Male Colorblind 8.0; Male Not Colorblind 52.0
D. Male Colorblind 6.0; Male Not Colorblind 53.0
Question 35
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 36
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.
Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
Question 37
A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed.
Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer's requirements. Use the partial t-table below to solve this problem.
Do not reject the null hypothesis. The data do not provide sufficient
evidence that the average distance is greater than 160 yards.
B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.
C. t= 1.2334; Critical value = 1.992
D. Insufficient information to answer this question.
Question 38
A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).
A. differ more than
B. differ less than
C. are equal to
D. do not vary with
Question 39
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
|
State the null and alternative hypothesis for the information above.
A.H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are related in some way.
B.H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are not related in any way.
C.H0: Colorblindness and gender are dependent characteristics.
Ha: Colorblindness and gender are not related in any way.
D.H0: Colorblindness and gender are independent characteristics.
Ha: Colorblindness and gender are related in some way.
Question 40
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.