Question

a manufacturer of bedding wants to do quality control on its 400 - thread - count sheets. the thread count varies normally with a mean thread count \\( \mu=400 \\) and a standard deviation \\( \sigma = 8 \\). a quality control researcher randomly selects 16 sheets and finds that the mean thread count for the sample is 395.2. we want to determine if these data provide enough evidence to conclude that the mean thread count is significantly different from the target level. one - sample z - test of \\( \mu = 400 \\) vs. \\( \mu\
eq400 \\) assumed standard deviation \\( = 8 \\) \\( n = 16 \\) mean \\( = 395.2 \\) z - value \\( = - 2.4 \\) two - tailed p - value \\( = 0.0164 \\) 95% confidence interval: \\( (396.0801,403.9199) \\) which of the following represents the correct conclusion we can make on the basis of the output (and at the usual significance level of 0.05)? a. the data provide enough evidence to reject \\( h_0 \\) and to conclude that the mean thread count is different than the target level of 400. b. the data provide enough evidence to accept \\( h_0 \\) and to conclude that the mean thread count is at the target level of 400. c. the data do not provide enough evidence to reject \\( h_0 \\), so we accept it, and conclude that the mean thread count is at the target level of 400. d. the data do not provide enough evidence to reject \\( h_0 \\) nor to conclude that the mean thread count is different than the target level of 400.

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the p - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, $\alpha = 0.05$ and the p - value is $0.0164$.

Step2: Compare the p - value and the significance level

Since $0.0164<0.05$, we reject the null hypothesis. The null hypothesis $H_0:\mu = 400$ and the alternative hypothesis $H_1:\mu
eq400$. Rejecting $H_0$ means we have enough evidence to support $H_1$.

Answer:

A. The data provide enough evidence to reject $H_0$ and to conclude that the mean thread count is different than the target level of 400.