Question

The mean age of the patrons of a particular nightclub has historically been 35 years. The proprietor of the nightclub wishes to find out if there is evidence that the mean age of his patrons has increased. Let μ be the mean age of the patrons of the nightclub.

Step 1: State the null and alternative hypotheses.

Step 2: A random sample of 41 recent evenings is selected. The average age of the patrons in the sample is 36.4 years with a standard deviation of 4.2 years. Find the test statistic. Give your answer to 3 decimal places.

Step 3: Ignore your answers in Steps 1 and 2. Assume that the test is one-sided and the statistic is 1.485. Find the P-value of the test. Give your answer to 3 decimal places.

Step 4: Ignore your answer in Step 3. Assume that the P-value is 0.028. We conclude at α = 5 % that:

Step 5: Find the critical value associated with a 95% confidence interval for μ . Give your answer to 3 decimal places.

Answer 1

1)

H0: = 35

Ha: > 35

2)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 36.4 - 35) / ( 4.2 / sqrt(41) )

= 2.134

3)

From T table,

With test statistics of 1.485 and df of 40,

p-value = 0.073

4)

Since p-value of 0.028 < 0.05 significance level , Reject the null hypothesis

5)

df = n - 1 = 41 - 1 = 40

t critical value at 0.05 significance level with 40 df = 2.021