For each of the following situations, carry out the appropriate hypothesis test.

Question

For each of the following situations, carry out the appropriate hypothesis test. Be sure to label all steps and draw real world conclusions.

Your factory manufactures a special cylindrical part of the Falcon 9 rocket. The diameter of the part must be 11 mm with a high degree of precision. SpaceX verifies individual components before installation, but to protect your reputation, you must ensure the mean diameter of the parts in a particular order is approximately 11 mm. If you randomly select 150 parts from the order and find a mean of 10.9 mm and standard deviation of 0.3mm, is this order sufficient to be shipped at a significance level = 0.01?

Explanation / Answer

we can conduct a z test to answer this question , as the sample size is greater than 40

given that

xbar = 10.9 , mu = 11 , n = 150 , sd = 0.3

so we use the formula

Z test = (xbar-mu)/(sd/sqrt(n)) =   (10.9-11)/(0.3/sqrt(150)) = - 4.08

now consider an alpha = 0.01 , we check the z critical value as

-2.32

also the p value from the z table is

0.000023 , which is less than alpha of 0.01 ,hence we can reject the null hypothesis and conclude that

H0 : mean diameter is not statistically different from 11mm

H1 :mean diameter is statistically different from 11mm

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