1. A. 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
B. Explain the meaning of a Type II error.
- Concluding that µ > 8.0 hours when in fact µ > 8.0 hours
- Failing to reject the hypothesis that µ = 8.0 hours when in fact µ > 8.0 hours
- Concluding that µ > 8.0 hours
- Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours
2. 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.
3. 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.
4. 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.
5. 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
6. 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.
7. 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
8. 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.
9. 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
10. 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
11. The __________ test statistic is for the one-way analysis of variance.
a. P-Value
b. t
c. C. F
d. D. p
12. 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
13. 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 3.427, 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.
14. 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
15. 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
Degrees of 0.025 0.05
Area in two tails
Freedom 0.05 0.10
n - 1
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.
16. 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
17. 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
18. 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
19. 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
20. 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
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 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.
22. 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
23. 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.
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.
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
24. 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.
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.
25. 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
26. 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.