Question

A production line is supposed to produce rulers that are 12 inches long. A sample of 49 rulers has mean of 12.1 inches, with standard deviation 0.5 inches. You, as a quality control consultant, are responsible for conducting a two-sided hypothesis test to determine whether the production line is really producing rulers that are 12 inches long or not. a) State the null and alternative hypotheses for the test. b) Conduct the hypothesis test and summarize the results in context of the problem. Be sure to clearly show your work.

Answer 1

Explanation:

`H_0: xbar  = 12\\H_a: x bar \\eq 12`

(Two tailed test at 0.05 significance level)

Given that sample parameters are(Mean =12.1,s= 0.5)

Since population std deviation is not known only t test can be used.

Mean difference = 12.1-12 =0.1

Std error =
`(0.5)/(√(49) ) =0.071`

Test statistic t = mean diff/se = 1.41

df =49-1 =48

p value = 0.1649

Since p >0.05 we accept null hypothesis.

There is evidence to confirm that the production line is really producing rulers that are 12 inches long