Question

A manufacturer of industrial bolts for riding mowers requires that a particular type of bolt be 8.00 mm. in diameter. Periodically, the company draws an SRS of 30 bolts from recent batches and measures them to determine whether the manufacturing process is producing the desired diameter. The null hypothesis is H₀: μ = 8.00. The alternative hypothesis is H_A: μ ≠ 8.00.

In the most recent sample, the mean diameter was 7.95 mm. and the sample standard deviation was 0.10 mm.

What is the P-value for the hypothesis test (to four decimal places of accuracy)?

Group of answer choices

0.0104

0.0792

0.1000

0.0500

0.0052

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 8.00

H_a : 8.00

Test statistic = t

= ( - ) / s / n

= (7.95 - 8.00) / 0.10 / 30 = -2.739

Test statistic = t = -2.739

df = n - 1 = 30 - 1 = 29

using t table

P-value = 0.0104