Question

A rods manufacturer makes rods with a length that is supposed to be 14 inches. A quality control technician sampled 33 rods and found that the sample mean length was 14.05 inches and the sample standard deviation was 0.27 inches. The technician claims that the mean rod length is more than 14 inches. What type of hypothesis test should be performed? What is the test statistic? What is the number of degrees of freedom? Does sufficient evidence exist at the α=0.01 significance level to support the technician's claim?

Answer 1

The type of hypothesis test will be one sample t-test. we use t-test when either the sample size is less than 30 or population standard deviation is not known or both. Here, population std dev. is not given (instead sample std dev is given), so we chose t test over normal z test.

Null hypothesis, Ho: mean = 14 inches

Alternative hypothesis, Ha: mean > 14 inches

The claim is the alternative hypothesis.

test statistic = observed (sample) mean - proposed (population) mean / standard deviation = (14.05 - 14) / 0.27 = 0.185

Number of degrees of freedom = n -1 = 33 - 1 = 32

significance level = 0.01

and it is a one tailed test. (As we have to test for 'greater than', means one sided)

P value (using calculator) = 0.427, shown below

So, if p value is greater than significance level, as is the case here, we fail to reject the null hypothesis. Means there is insufficient evidence at 0.01 significance level to support the technician's claim.

Thumbs up please!