Question

A piston in a particular 12-cylinder diesel engine is manufactured to have diameter 13 mm. Every half-hour, 10 finished pistons are selected and carefully measured. If there is any evidence that the mean diameter is different from 13 mm, the manufacturing process must be stopped for the machine to be inspected.

The quality control inspector uses a significance level of 0.05 and found the sample to have a mean of 12.8 mm and a standard deviation of 0.06 mm.

A) State the null and alternate hypothesis (either sentence or symbolic for will be accepted) for testing if the machine is working.

B) Which test was used, and what was the p-value?

Which test was used, and what was the p-value?

T-Test, p=1

Z-Test, p=0

T-Test, p=0

Z-Test, p=1

C) Draw a conclusion about the need for the machine to be inspected. Give justifications and include an interpretation of the possible Type I Error.

Answer 1

A.Here claim is that mean is 13

So hypothesis is vs

B. Here n=10<30, and population standard deviation is not known we will use t distribution

P value is TDIST(10.54,9,2)=0

So answer is

T-Test, p=0 c. As P value is less than alpha we reject the null hypothesis Hence we do not have sufficient evidence to support the claim that mean is equal to 13 In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding). So here interpretation of the possible Type I Error is that actually mean is 13 but we concluded that it is different from 13