Question

A research service estimates that the mean annual consumption of fresh-market tomatoes by a person in the United States is less than 25 pounds. A random sample of 65 people in the United States has a mean annual consumption of fresh-market tomatoes of 22 pounds and a population standard deviation of 6 pounds. At α = 0.05, is there enough evidence to reject the service’s claim?

a. Identify the claim and state H₀ and H_a.

b. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

c. Find the critical value(s) and identify the rejection region(s).

d. Find the standardized test statistic z or t.

e. Decide whether to reject or fail to reject the null hypothesis.

f. Interpret the decision in the context of the original claim

Answer 1

Part a)

To Test :-
H0 :- µ >= 25
H1 :- µ < 25

Part b)

left-tailed test

Part c)

Critical value Z(α) = Z(0.05) = 1.645 ( From Z table )

Part d)

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 22 - 25 ) / ( 6 / √( 65 ))
Z = -4.0311

Part e)

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z < -Z(α) = -4.0311 < -1.645
Result :- Reject null hypothesis

Part f)

There is sufficient evidence to support the claim that the mean annual consumption of fresh-market tomatoes by a person in the United States is less than 25 pounds.