Question

In: Statistics and Probability

The diameter of holes for cable harness is known to have a standard deviation of 0.01...

The diameter of holes for cable harness is known to have a standard deviation of 0.01 in. A random sample of size 10 yields an average diameter of 1.5045 in. Use α=0.01 to:

a. Test the hypothesis that the true mean whole diameter equal 1.5 in.

b. What sample size would be necessary to detect a true mean hole diameter of 1.505 in. with probability of at least 0.95?

c. What is the type II error if the true mean hole diameter is 1.504 in.?

Solutions

Expert Solution

It should be noted that as the sample size increases, the sample mean tends toward the population mean. Hence, the confidence interval size is large when n is small for a given probability ( i.e. we are more unsure of the mean).

The extreme points of this interval represent the critical values for the sampled mean.

orchestra answered 1 year ago
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