A local eat-in pizza restaurant wants to investigate the possibility of starting

Question

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries docs not exceed 34 minutes. The owner has randomly selected 23 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 34 minutes. Suppose the P-value for the test was found to be 0.0284. State the correct conclusion. A) At alpha = 0.03, we fail to reject H_0. B) At alpha = 0.05, we fail to reject H_0. C) At alpha = 0.025, we fail to reject H_0. D) At alpha = 0.02, we reject H_0 A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. At alpha = 0.05, test the trucking firm's claim.

Explanation / Answer

Solution of 20:

H0 : variance <= 1,000,000
H1 : variance > 1,000,000

Rejection Region : Xo^2 > X^2

s = 1200
test statistic, Xo^2 = (n-1)s^2/1000000 = 100*(1200)^2/1000000 = 144

alpha = 0.05
X^2 = X^2(alpha,n-1) = X^2(0.05,100) = 124

since Xo^2 > X^2
=> null hypotheses can be rejected and
=> the claim that the variance is greater than 1,000,000 is TRUE

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