Question

A manufacturer wants to test the lifetime of a small motor it builds; the mean lifetime is supposed to be at least 4 years. Assume that the distribution of lifetimes is approximately normal. (a) The manufacturing unit will do a thorough investigation of the manufacturing process if it has reason to believe that the lifetime is too short. Formulate a null and alternative hypothesis. (b) The CEO has called and said that selling substandard motors is unacceptable. Now an investigation will be done unless there is evidence that the mean lifetime meets requirements. Formulate a null and alternative hypothesis. (c) A random sample of 15 motors is made. Under the situation of part (b), and with a signicance of 0.05, formulate the test procedure. (d) Suppose that the sample mean is 4.13 years and the sample standard variation is 0.35 years. What does the test procedure in part (c) say to do?

Answer 1

n = 15

$\bar{x}=4.13$

s = 0.35

Claim: Null and alternative hypothesis is

H0 : u = 4

H1 : u $\geq$ 4

Level of significance = $\alpha$ = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

$t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}$

$t=\frac{4.13-4 }{\frac{0.35}{\sqrt{15}}}$

$t=1.4385$

Degrees of freedom = n - 1 = 15 - 1 = 14

$\alpha$? = 0.05

P-value = 0.086 ( using t table)

P-value >$\alpha$ , Failed to Reject H0