A random sample of 100 observations from a quantitative population produced a sample mean of 29.7 and a sample standard deviation of 7.8. Use the p-value approach to determine whether the population mean is different from 31. Explain your conclusions. (Use = 0.05.)

Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z	=
p-value	=

2. Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study looked at the diameter (in mm) of the affected tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of 5.96 millimeters (mm). When the diameters of the affected tendon were measured for a random sample of 33 patients, the average diameter was 9.50 with a standard deviation of 1.92 mm. Is there sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.96 mm? Test at the 5% level of significance.

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statistic	z =
rejection region	z >
	z <

You may need to use the appropriate appendix table or technology to answer this question.

3. Independent random samples of n₁ = 160 and n₂ = 160 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 74 successes, and sample 2 had 81 successes.

(b) Calculate the standard error of the difference in the two sample proportions, (p₁ p₂). Make sure to use the pooled estimate for the common value of p. (Round your answer to four decimal places.) (c) Calculate the test statistic that you would use for the test in part (a). (Round your answer to two decimal places.) z =

(d) p-value approach: Find the p-value for the test. (Round your answer to four decimal places.) p-value =

(e) Critical value approach: Find the rejection region when = 0.01. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z	>
z	<