Question

A manufacturer of industrial bolts for riding mowers requires that a particular type of bolt be 12.0 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: $\mu=12.0$ μ=12.0. The alternative hypothesis is H_A: $\mu\ne12.0$ μ≠12.0.

In the most recent sample, the mean diameter was 12.03 mm. and the sample standard deviation was 0.12 mm.

What is the value of the one-sample t-statistic?

Round your answer to 2 decimal places of accuracy.

Answer 1

Solution :

Given that

$\mu$ = 12.0

$\bar x$ = 12.03

S = 0.12

n = 30

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ : $\mu$ = 12.0

H_a : $\mu$    $\neq$ 12.0

Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (12.03 - 12.0 ) /0.12 / $\sqrt$ 30

= 13.693

Test statistic = t = 13.69