Reference no: EM13763034
Question 1
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 2
| Number of Peanuts per bag |
Probability |
| 25 |
0.006 |
| 30 |
0.02 |
| 35 |
0.093 |
| 40 |
0.15 |
| 45 |
0.35 |
| 50 |
0.217 |
| 55 |
0.17 |
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
Question 3
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 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 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 6
A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers. Use Table 5.1 to find the best answer.
A. 0.0559
B. 0.1118
C. 0.0252
D. 0.0505
Question 7
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 8
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 9
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 = 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 10
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 11
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 12
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 13
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 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 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 16
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 17
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 18
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 19
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 a : µ ¹ 18.4 hours
B. Ho: µ = 18.4 hours H a : µ < 18.4 hours
C. Ho: µ ³ 18.4 hours H a : µ < 18.4 hours
D. Ho: µ = 18.4 hours H a : µ > 18.4 hours
Question 20
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 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
|
Find the value of the χ2 statistic for the data above.
A. 1.463
B. 1.852
C. 1.947
D. 1.949
Question 22
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 23
Which of the following statements is true?
A. 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 24
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. State the null and alternative hypotheses for this test.
A. H0: µ = 180; Ha: µ > 180
B. H0: µ > 180; Ha: µ > 180
C. H0: µ < 180; Ha: µ > 180
D. H0: µ = 180; Ha: µ < 180
Question 25
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 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.
A. Smaller. E decreases as the square root of the sample size gets larger.
B. Smaller. E increases 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 26
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 27
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 28
The critical value of χ 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ 2 statistic in Problem 8 had been 3.179, state your conclusion about the relationship between gender and colorblindness.
A. Do not reject H0.
B. Reject H0.
C. 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 29
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 30
The following data were analyzed using one-way analysis of variance.
A B C
34 27 19
26 23 21
31 29 22
28 21 12
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 31
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.
Area in one tail
0.025 0.05
Area in two tails
Degrees of
Freedom
n - 1 0.05 0.10
6 2.447 1.943
7 2.365 1.895
8 2.306 1.860
9 2.262 1.833
A. 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 32
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 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.
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.
|
|
Area in one tail
|
|
|
0.025
|
0.05
|
|
|
Area in two tails
|
|
Degrees of
Freedom
n - 1
|
0.05
|
0.10
|
|
6
|
2.447
|
1.943
|
|
7
|
2.365
|
1.895
|
|
8
|
2.306
|
1.860
|
|
9
|
2.262
|
1.833
|
A. 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 34
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 35 :
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 36 :
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 37
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 38
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 #21 had been 4.613, state your conclusion about the relationship between gender and colorblindness.
A. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C. Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
D. Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
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
|
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 40
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.
|
|
Area in one tail
|
|
|
0.025
|
0.05
|
|
|
Area in two tails
|
|
Degrees of
Freedom
n - 1
|
0.05
|
0.10
|
|
6
|
2.447
|
1.943
|
|
7
|
2.365
|
1.895
|
|
8
|
2.306
|
1.860
|
|
9
|
2.262
|
1.833
|
A. 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 gre