Question

The mean age of the patrons of a particular nightclub has historically been 35 years. The proprietor of the nightclub wishes to determine if the mean age of his patrons has changed. He uses a sample of 36 recent evenings and finds that the average age of the patrons in the sample is 36.8 years in the standard deviation of 3. 6 years. Let u be the mean of the patrons of the nightclub.

1) State the null and alternative hypothesis
2) Find the P value of the test. Give your answer to three decimal places.
3) we conclude a x=5% that

Answer 1

a) As we are testing here that the mean has changed from 35 years, therefore the null and the alternate hypothesis here are given as:

b) The test statistic here is computed as:

Now as this is a two tailed test, for n-1 = 35 degrees of freedom, the p-value here is computed as:

p = 2P( t₃₅ > 3 ) = 2*0.0025 = 0.005

Therefore 0.005 is the required p-value here.

c) At a significance level of 5% that is 0.05, we see here that the p-value is 0.005 < 0.05, therefore the test is significant and we can reject the null hypothesis here and conclude that the mean has changed significantly from the mean of 35 years.