Question

Use an α = 0.05 significance level to test the claim that the mean wait time at a particular restaurant exceeds 15 minutes. A sample of 30 customers had an average wait time of 16.5 minutes. Assume σ 2 minutes. 1.

Answer 1

Here null hypothesis is

Ho: t= 15

Against alternative hypothesis

Ha: t> 15

Where t is mean wait time at restaurant

Since sample size n=30 is quite large, we use z test

Test statistic is

Z = (tbar- t)/ (sigma/sqrt(n))

= (16.5-15)/ ( 2/sqrt(30))

= (1.5*5.477) / 2

= 4.1077

Critical value is one tailed z value at 95% confidence, which is 1.645. Since test statistic is greater than critical value, we reject Ho at 5% and conclude waiting time at restaurant is greater than 15 minutes.