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# Average Peak Heights for the Mean Times

1. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?

2. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.6 seconds. Suppose that you want to set up a statistical test to challenge the claim of 8.6 seconds. What would you use for the null hypothesis?

3. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.4 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 6.4 seconds. What would you use for the alternative hypothesis?

4. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.4 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 6.4 seconds. What would you use for the alternative hypothesis?

5. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 8.7 seconds. What would you use for the alternative hypothesis?

6. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.6 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is different than 7.6 seconds. What would you use for the alternative hypothesis?

7. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 15 Australian bank stocks has a mean For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.1%? Use What is the level of significance?

8. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 18 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.5%? Use What is the value of the test statistic?

9. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 23 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.7%? Use Find (or estimate) the P-value.

10. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 24 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 9.3%? Use If the sample test statistic find (or estimate) the P-value.

11. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 17 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.7%? Use Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?

12. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 17 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6%? Use If the P-value is 0.045, are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?

13. When using the student's t distribution to test what value do you use for the degrees of freedom if the sample size is 42?

14. Consider a test for If the P-value is such that you can reject at the 5% level of significance, can you always reject at the 3% level of significance?

15. If sample data is such that for a one-tailed test of you can reject at the 2% level of significance, can you always reject for a two-tailed test at the same level of significance?

16. A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect? Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What is the level of significance?

17. A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 48 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect? Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What are the null and alternate hypotheses?

18. A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 45 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect? Use a 5% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What is the value of the test statistic?

#### Solution Preview

A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?

Solution:

Alternate Hypothesis: The mean wave height is less than 16.4 feet.
H_a: μ<16.4

The given test is a left-tailed test (lower-tailed test) and thus the P-value area is on the left side of the mean.

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.6 seconds. Suppose that you want to set up a statistical test to challenge the claim of 8.6 seconds. What would you use for the null hypothesis?

Solution:

Null Hypothesis: The mean time for the car to go from 0 to 60 miles per hour is equal to 8.6 seconds.
H_0: μ=8.6

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.4 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 6.4 seconds. What would you use for the alternative hypothesis?

Solution:

Alternate Hypothesis: The mean time for the car to accelerate from 0 to 60 miles per hour is greater than 6.4 seconds.
H_a: μ>6.4

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.4 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 6.4 seconds. What would you use for the alternative hypothesis?

Solution:

Alternate Hypothesis: The mean time for the car to accelerate from 0 to 60 miles per hour is greater than 6.4 seconds.
H_a: μ>6.4

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 8.7 seconds. What would you use for the alternative hypothesis?

Solution:

Alternate Hypothesis: The mean time for the car to accelerate from 0 to 60 miles per hour is less than 8.7 seconds.
H_a: μ<8.7

Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.6 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is different than 7.6 seconds. What would you use for the alternative hypothesis?

Solution:

Alternate Hypothesis: The mean time for the car to accelerate from 0 to 60 miles per hour is not equal to 7.6 seconds.
H_a: μ≠7.6

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample ...

#### Solution Summary

The average peak heights for the mean times are examined.

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