Question

a fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 927 milligrams. a random sample of 39 breakfast sandwiches has a mean sodium content of 919 milligrams. assume the population standard deviation is 16 milligrams. at \\( \alpha = 0.10 \\), do you have enough evidence to reject the restaurants claim? complete parts (a) through (e).

(d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

○ a. fall to reject \\( h _ { 0 } \\). there is not sufficient evidence to reject the claim that mean sodium content is no more than 927 milligrams. ○ b. fall to reject \\( h _ { 0 } \\). there is sufficient evidence to reject the claim that mean sodium content is no more than 927 milligrams.

○ c. reject \\( h _ { 0 } \\). there is not sufficient evidence to reject the claim that mean sodium content is no more than 927 milligrams. ○ d. reject \\( h _ { 0 } \\). there is sufficient evidence to reject the claim that mean sodium content is no more than 927 milligrams.

Explanation:

To decide whether to reject or fail to reject the null hypothesis, we compare the test - statistic (not shown in the problem, but assuming standard hypothesis - testing procedures for a one - sample z - test since the population standard deviation is known). If the test - statistic is in the non - rejection region (based on the significance level \(\alpha = 0.10\) for a one - tailed test), we fail to reject \(H_0\). Failing to reject \(H_0\) means there is not enough evidence to go against the original claim.

Answer:

A. Fall to reject \(H_{0}\). There is not sufficient evidence to reject the claim that mean sodium content is no more than 927 milligrams.