# In the past, the mean running - Expert Answers

1.         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
2.         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.
3.         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%
4.         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
5.         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
6.         The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. 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 mean attendance is greater than 3000.
B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.
C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.
D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.
7.         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
8.         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.
A. 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.
9.         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.
10.       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
11.       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.
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 Democrats.
13.       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
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.
15.       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.
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
17.       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 null and alternative hypotheses for the test described.
A.H0: µ = 16 ounces     Ha: µ < 16 ounces
B. H0: µ ¹ 16 ounces     Ha: µ = 16 ounces
C. H0: µ = 16 ounces     Ha: µ 16 ounces
D. H0: µ = 16 ounces      Ha: µ ¹ 16 ounces
18.       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
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
20.       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
21.         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
22.       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
Find the value of the X2 statistic for the data above.
A. 1.325
B. 1.318
C. 1.286
D. 1.264
23.       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
24.       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.
25.       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
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    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
27.       The __________ test statistic is for the one-way analysis of variance.
A. P-Value
B. t
C. F
D. p
28.       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
29.       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
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 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.
31.       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
32.       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.
33.       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.
34.       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.
35.       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.
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 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
37.       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
38.       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.
39.       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 x̄ 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
40.       A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?
A. 2.0
B. 2.7
C. 3.0
D. 4.0