Question

In: Statistics and Probability

A factory that manufactures bolts is performing a quality control experiment. Each object should have a...

A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 17 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 56 bolts. The sample mean bolt length was 17.04 centimeters. The population standard deviation is known to be σ=0.22 centimeters. What is the test statistic z? What is the p-value? Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of α=0.01?

Note: I still don't quite understand how you get the p-value and When I do the math I get a different result when using the formula. The whole concept of hypothesis testing is confusing so hopefully someone can give a detailed explanation. Thank You

Solutions

Expert Solution

Null Hypothesis:

It states that object should a length of no more than 17 centimeters.

Alternate Hypothesis (claim: opposite of null Hypothesis):

It states that the length of bolts is actually greater than the mean value.

Tail-test: Right tailed test because of '>' sign.

Sample size n = 56

Sample mean = 17.04

population sd 0.22

Ans i) Test statistics:

Therefore, the test statistic z = 1.36

Ans ii)

P-value = 0.0869

P-value > (Fail to reject null hypothesis)

/* we can find P-value using excel function: =1-NORM.S.DIST(1.36,TRUE) we subtract it from 1 because of right tailed test */

P-value using z-table:

1 - 0.9131 = 0.0869

Conclusion: There is not sufficient evidence to support the claim that the length of bolts is actually greater than the mean value at a significance level of α=0.01.

/* PLEASE UPVOTE */


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