4 A statistician selected a sample of 16 accounts receivable

4. A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. He reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. He neglected to report what confidence coefficient he had used. Based on the above information, determine the confidence coefficient that was used. Assume the population has a normal distribution.

Solution

The formula for CI for normal distribution is:

Mean plus minus z*(sd/sqrt n)

Thus, 5000+z*(400/sqrt16)=4739.80

Z*(100)=-260.2

Z*=2.602

Thus the confidence coefficient z* is 2.602