Question

Make sure to show all steps to receive full credit, that is: a) Identify the claim: state the null and alternative hypotheses. b) Determine the test: left-tailed, right-tailed, or two-tailed. c) Graph your bell-shaped curve and label your levels of significance or critical value. d) Find your standardized test statistic ? and label it on your graph. e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret your result.

1) A dealership projected that the mean lifetime of a certain brand of tire of uses is less than 32,000 miles. To check the claim, the dealership randomly selects and tests 38 of these tires and gets a mean lifetime of 31,250 miles with a population standard deviation of 9,000 miles. At α = 0.05, test the dealership’s claim.

Answer 1

The hypothesis being tested is:

H₀: µ = 32000

H_a: µ < 32000 (Claim)

This is a left-tailed test.

The curve is:

The test statistic, z = (x - µ)/σ/√n

z = (31250 - 32000)/9000/√38

z = -0.51

The p-value is 0.3037.

Since the p-value (0.) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the mean lifetime of a certain brand of tire of uses is less than 32,000 miles.

Please give me a thumbs-up if this helps you out. Thank you!