Question

A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for "reduced sodium" franks. The lab failed to reject the hypothesis that the hot dogs did not meet this requirement, with a P-value of 0.142. A 90% confidence interval estimated the mean sodium content for this kind of hot dog at 317.2 to 326.8 mg. Explain how these two results are consistent. Your explanation should discuss the confidence level, the P-value, and the decision.

Answer 1

Answer:

Null hypothesis is rejected in 90% confidence level.

Step-by-step explanation:

Hypotheses are:

$H_{0}:$ mean sodium content is  325-mg

$H_{a}:$ mean sodium content is less than 325-mg

At 90% confidence level p(critical)=0.10 and

Since  P-value = 0.142 > 0.10, we fail to reject the null hypothesis that the hot dogs do not meet this requirement (less than 325-mg)

This result is consistent with the confidence interval 317.2 to 326.8 mg at 90% confidence level, since confidence interval includes upper limit 325-mg set by regulations for "reduced sodium" franks.