HW 7.5

#1 Use a ²-test to test the claim ²=0.51 at the =0.05 significance level using sample statistics s²=0.522 and n=21.

Assume the population is normally distributed.

(a) Identify the null and alternative hypotheses.

(b) Identify the test statistic.

(c) Identify the critical value(s).

(d) Interpret the results.

#2 Use a ²-test to test the claim < 41 at the =0.01 significance level using sample statistics s=40.7 and n=17.

(a) Identify the null and alternative hypotheses.

(b) Identify the test statistic.

(c) Identify the critical value(s).

(d) Interpret the results.

#3 Quarters are currently minted with weights normally distributed and having a standard deviation of 0.065. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.043. Use a 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.065. Does the new equipment appear to be effective in reducing the variation of weights?

(a) Write the claim mathematically and identify H_o and H_a.

(b) Find the critical value(s)

(c) Use the ²-test to find the standardized test statistic

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

#4 Use a 0.025 significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is 0.492. A sample of 71 peanut candies has weights with a standard deviation of 0.29.

Assume the population is normally distributed.

(a) Write the claim mathematically and identify H_o and H_a.

(b) Find the critical value(s)

(c) Use the ²-test to find the standardized test statistic

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

#5 Use a 0.05 significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is 0.159. A sample of

71 peanut candies has weights with a standard deviation of 0.31.

Assume the population is normally distributed.

(a) Write the claim mathematically and identify H_o and H_a.

(b) Find the critical value(s)

(c) Use the ²-test to find the standardized test statistic

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

#6 A hospital spokesperson claims that the standard deviation of the waiting times experienced by patients in its minor emergency department is no more than 0.7 minutes. A random sample of 25

waiting times has a standard deviation of 1.1 minutes. At =0.05, is there enough evidence to reject the spokesperson's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.

(a) Write the claim mathematically and identify H_o and H_a.

(b) Find the critical value(s)

(c) Use the ²-test to find the standardized test statistic

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.