A random sample of size 100 from a non-normal population yielded the sample valu

Question

A random sample of size 100 from a non-normal population yielded the sample values of a sample mean of 300 and sample variance of 900. Find an approximate 95% confidence interval for the population mean. Interpret this result. An important manufacturing process produces cylindrical component parts for the automotive industry. It is important that the process produce parts have a mean diameter of 5 millimeters. The engineer involved conjectures that the population mean is 5 millimeters. An experiment is conducted in which 100 parts produced by the process are selected randomly and the diameter is measured on each. It is known that the population standard deviation is 0.1. The experiment indicates a sample average diameter of 5.025 millimeters. Does this sample information appear to support or refute the engineer's conjecture? Explain using statistical analysis.

Explanation / Answer

9)

n=100 => sqrt(n)=10

X=300

variance=900=>s=30

95% confidence interval

=>z=1.96

So C.I is (300 - 1.96*30/10 , 300 + 1.96*30/10 ) = (241.2, 358.8)

10)

Ho:mean is 5mm

Ha: Mean is not 5mm

n=100 =>sqrt(n)=10

s=0.1

X=5.025

Use Z test

z= (5.025-5)/0.1/10

look at the z table and compare with critical z value

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