The National Collegiate Athletic Association ( NCAA) reportedthat the mean numbe

Question

The National Collegiate Athletic Association ( NCAA) reportedthat the mean number of hours spent per week on coaching andrecruiting by college football assistant coaches during the seasonwas 70.

A random sample of 50 assistant coaches showed the sam-ple meanto be 68.6 hours, with a standard deviation of 8.2 hours. a. Usingthe sample data, construct a 99 percent confidence interval for thepopulation mean.

b. Does the 99 percent confidence interval include thevalue suggested by the NCAA? Interpret this result.

c. Suppose you decided to switch from a 99 to a 95 percentconfidence interval. With-out performing any calculations, will theinterval increase, decrease, or stay the same? Which of the valuesin the formula will change?

Explanation / Answer

Z(0.01/2)=Z(0.005)=3.3, so 99% confidence interval is

(68.6-Z(0.005)*8.2/sqrt(50), 68.6+Z(0.005)*8.2/sqrt(50))=(64.77,72.43)

Yes. It mens that the conclusion that the mean number of hoursspent per week on coaching and recruiting by college footballassistant coaches during the season is 70 is correct.

Since Z(0.05/2)<Z(0.01/2) and other values will not change,then the interval will become shorter.

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