A linen company produces bed sheets that they claim are 800 thread count on aver

Question

A linen company produces bed sheets that they claim are 800 thread count on average. You try them out, and you think that they feel a bit thin to have an average thread count of 800. You look at 40 other randomly selected sets of sheets from this company and examine their thread counts. You find that they average a thread count of 750 with a variance of 100 (thread count)2 .

In the sets of sheets, you observe that there appears to he a lot of discrepancy in the thread counts. Ideally, the variance of the thread counts would he around 50 (thread count)2. Is there evidence at the 0.01 significance level that the variance of the thread counts differs from 50? Carry out a complete hypothesis test to answer this question.

Explanation / Answer

Ho : sigma^2 = 50

Ha : sigma^2 is not 50

X^2 = 100 * 39 / 50 = 78

for alpha = 0.01 df= 39   critical value is 63.691

since X^2 > critical value we conclude that the variance of the thread counts differs form 50

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