A company makes leather belts. The length of one particular belt is designed to

Question

A company makes leather belts. The length of one particular belt is designed to be 26 inches. The company test for quality control, and if the mean length is found to be significantly longer or shorter than 26 inches, the machines get adjusted. The most recent random sample of 28 belts had a mean length of 26.3 inches with a standard deviation of 0.77 inches. Perform a hypothesis test to determine if the length differs from 26 inches at a 95% confidence level. The population standard deviation is not know. State the null & alt hypothesis, and all values. State your conclusion.

Explanation / Answer

Ho : miu = 26    H1 : miu is different from 26

t = ( 26.3 - 26 ) / ( 0.77 / srqt 28 )

t = 2.06

for alpha / 2 = 0.025 df = 27

critical value : +/-2.052

since t > critical value we reject Ho

conclusion

the lenght differs from 26 inches

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