The owner of a local nightclub has recently surveyed a random sample of n = 250

Question

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make? B)ALso, what rejection region should be used? C)what is the p value associated with the test statistic? I need to explain how I obtained the answer -and PhStat.

Explanation / Answer

alpha / 2 = 0.005 Z = 2.57

I: 30.45 +/- 2.57 * 5 / srqt 250

30.45 +/- 0.8127

29.6373 < miu < 31.2627

b)

rejection region wll be alpha = 0.01 rject if Z or t >2.57 or < -2.57

c)

p value

you can obtain p value from table of normal distribution for example

Ho : miu = 30 Ha : miu is not 30

Z = ( 30.45 - 30 ) / ( 5 / srqt 250 )

Z = 1.423

p value : 0.0773

since p value is greater than .0.01 we fail to reject Ho

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