Question

Hypothesis Testing Using Rejection Region(s). In Exercises 37–42, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim.

39. Fast Food A fast-food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams. A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams. Assume the population standard deviation is 18 milligrams. At a = 0.10, do you have enough evidence to reject the restaurant’s claim?

Answer 1

a)

claim is HA: mu > 920

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 920
Alternative Hypothesis, Ha: μ > 920

b)

This is right tailed test, for α = 0.1
Critical value of z is 1.28.
Hence reject H0 if z > 1.28

c)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (925 - 920)/(18/sqrt(44))
z = 1.84

d)
Reject h0

e)

There is sufficient evidence to conclude that the mean sodium content in one of its breakfast sandwiches is no more than 920 milligrams.