Question

A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than 15 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 75 bolts. The sample mean bolt length was 15.07 centimeters. The population standard deviation is known to be a = 0.26 centimeters. What is the test statistic z? Ex: 1.23 What is the p-value? Ex. 0.123 Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of a 0.01? ​

Answer 1

The test statistic z  is 2.33, the p-value corresponding to the test statistic z value is 0.0099.

What is Probability?

Probability is the measure of the likeliness of happening of an event.

The mean of the data is 15.07 centimeters

The standard deviation of the data is 0.26 centimeters.

n = 75

Significance Level ∝ = 0.01

According to the null and alternative hypothesis

Hₐ : $\rm \mu$ ≤15  vs H₁ : $\rm \mu$ >15

The test statistic z  is given by

$\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}$

Z = ( 15.07 -15)/(0.26/√75)

Z = 2.33

The p-value corresponding to z value is 0.0099

as p-value < significance level, therefore the H₁ : $\rm \mu$ >15 is acceptable.

No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.

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