Question

Let X denote the waiting time (in minutes) for a customer. An assistant manager claims that μ, the average waiting time of the entire population of customers, is 3 minutes with standard deviation also 2 minutes. The manager doesn't believe his assistant's claim, so he observes a random sample of 36 customers. The average waiting time for the 36 customers is 3.2 minutes. What is the probability that the average of 36 customers is 3.2 minutes or more? Do you think that assistant manager's claim that the mean is 3 minutes is correct?

Answer 1

Let X denote the waiting time (in minutes) for a customer. An assistant manager claims that μ, the average waiting time of the entire population of customers, is 3 minutes with standard deviation also 2 minutes.

so here hypothesis are

H₀ :  μ = 3 minutes

H_a : μ 3 minutes

Here standard deviation = 2 mins

sample size = n = 36

standard error = 2/sqrt(36) = 1/3 mins

test statitic

z = (3.2 - 3)/(1/3) = 0.6

so here p - value = 2 * P(z > 0.6)

looking into z table

p - value = 2 * (1 - 0.7257) = 0.5485

so here p- value > 0.05 so we would reject the null hypothesis and conclude that the mean of 3 minutes is correct.