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CHAPTER 7 Hypothesis Testing Because the value of the test statistic does not fall in the rejection region, we cannot reject H0 at 5% level of significance. Here, we assumed that the 25 cholesterol measurements follow the normal distribution. EXERCISES 7.4 7.4.1 A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64. (a) Is there sufficient evidence to refute the claim at the 2% level of significance? (b) What is the p-value? (c) What is the smallest value of ? for which the claim will be rejected? 7.4.2 A machine in a certain factory must be repaired if it produces more than 12% defectives among the large lot of items it produces in a week. A random sample of 175 items from a week's production contains 45 defectives, and it is decided that the machine must be repaired. (a) Does the sample evidence support this decision? Use ? = 0.02. (b) Compute the p-value. 7.4.3 A random sample of 78 observations produced the following sums: ? xi = 22.8, ?(xi ? x?)² = 2.05. (a) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? < 0.45 using ? = 0.01. Also find the p-value. (b) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? > 0.45 using ? = 0.01. Also find the p-value. (c) What assumptions did you make for solving (a) and (b)? Consider the test H0: ? = 35 vs Ha: ? > 35 for a population that is normally distributed. (a) A random sample of 18 observations taken from this population produced a sample mean of 40 and a sample standard deviation of 5. Using ? = 0.025, would you reject the null hypothesis? (b) Another random sample of 18 observations produced a sample mean of 40 and a sample standard deviation of 5.

          CHAPTER 7 Hypothesis Testing
Because the value of the test statistic does not fall in the rejection region, we cannot reject H0 at 5% level of significance. Here, we assumed that the 25 cholesterol measurements follow the normal distribution.
EXERCISES 7.4
7.4.1 A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64.
(a) Is there sufficient evidence to refute the claim at the 2% level of significance?
(b) What is the p-value?
(c) What is the smallest value of ? for which the claim will be rejected?
7.4.2 A machine in a certain factory must be repaired if it produces more than 12% defectives among the large lot of items it produces in a week. A random sample of 175 items from a week's production contains 45 defectives, and it is decided that the machine must be repaired.
(a) Does the sample evidence support this decision? Use ? = 0.02.
(b) Compute the p-value.
7.4.3 A random sample of 78 observations produced the following sums:
? xi = 22.8, ?(xi ? x?)² = 2.05.
(a) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? < 0.45 using ? = 0.01. Also find the p-value.
(b) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? > 0.45 using ? = 0.01. Also find the p-value.
(c) What assumptions did you make for solving (a) and (b)?
Consider the test H0: ? = 35 vs Ha: ? > 35 for a population that is normally distributed.
(a) A random sample of 18 observations taken from this population produced a sample mean of 40 and a sample standard deviation of 5. Using ? = 0.025, would you reject the null hypothesis?
(b) Another random sample of 18 observations produced a sample mean of 40 and a sample standard deviation of 5.

CHAPTER 7 Hypothesis Testing
Because the value of the test statistic does not fall in the rejection region, we cannot reject H0 at 5% level of significance. Here, we assumed that the 25 cholesterol measurements follow the normal distribution.
EXERCISES 7.4
7.4.1 A random sample of 50 measurements resulted in a sample mean of 62 with a sample standard deviation 8. It is claimed that the true population mean is at least 64.
(a) Is there sufficient evidence to refute the claim at the 2% level of significance?
(b) What is the p-value?
(c) What is the smallest value of ? for which the claim will be rejected?
7.4.2 A machine in a certain factory must be repaired if it produces more than 12% defectives among the large lot of items it produces in a week. A random sample of 175 items from a week's production contains 45 defectives, and it is decided that the machine must be repaired.
(a) Does the sample evidence support this decision? Use ? = 0.02.
(b) Compute the p-value.
7.4.3 A random sample of 78 observations produced the following sums:
? xi = 22.8, ?(xi ? x?)² = 2.05.
(a) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? < 0.45 using ? = 0.01. Also find the p-value.
(b) Test the null hypothesis that ? = 0.45 against the alternative hypothesis that ? > 0.45 using ? = 0.01. Also find the p-value.
(c) What assumptions did you make for solving (a) and (b)?
Consider the test H0: ? = 35 vs Ha: ? > 35 for a population that is normally distributed.
(a) A random sample of 18 observations taken from this population produced a sample mean of 40 and a sample standard deviation of 5. Using ? = 0.025, would you reject the null hypothesis?
(b) Another random sample of 18 observations produced a sample mean of 40 and a sample standard deviation of 5.

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