A researcher claims that the mean sodium content of chicken sandwiches at Restaurant A is less than the mean sodium content of chicken sandwiches at Restaurant B. The mean sodium content of 22 randomly selected chicken sandwiches at Restaurant A is 670 milligrams. Assume the population standard deviation is 20 milligrams. The mean sodium content of 28 randomly selected chicken sandwiches at Restaurant B is 690 milligrams. Assume the population standard deviation is 30 milligrams. At α = 0.05, is there enough evidence to support the researcher’s claim?

(a) Identify the claim and state H₀ and H_a,

(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,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.