Question

Assume we want to test the claim that the mean attendance in the arena is more than 20,000 fans. In order to test this we selected 8 concerts at random and took the attendance from each concert. The sample average from those 8 concert was 20,450. If we assume that we know the sample standard deviation is 500 fans. Show all 6 steps in conducting a hypothesis test to test this claim as a normal distrubution. Include the appropriate confidence interval in the conclusion. b. Conduct the test again showing all 6 steps accept assume now that we know sigma and that the value given is s = 500 fans .

Answer 1

H₀:  = 20000

H₁: > 20000

The test statistic is

= 2.55

At 0.05 significance level, the critical value is z_crit = 1.645

Since the test statistic value is greater than the critical value (2.55 > 1.645), so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to support the claim that the mean attendance in the arena is more than 20,000 fans.

At 95% Confidence level, the critical value is z_0.025 = 1.96

The 95% confidence interval is

= 20103.52, 20796.48