Question

The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes

Answer 1

Answer:

Yes, we can conclude that the mean waiting time is less than 3 minutes.

Step-by-step explanation:

Since we want to check if the average waiting time is less than 3 minutes, we can state the statistical hypothesis as follows:

$H_{0} :$ µ≥3

$H_{a}:$ µ<3

The test is a lower sided.

Now we calculate the test statistic z:

z=(x-µ)/(σ/$\sqrt{n}$)

=(2.75-3)/(1/$\sqrt{50}$)

=-1.7678

The p-value obtained from the standard normal table is 0.0386

Since the p-value is less than the significance level (0.0386<0.05), the decision is to reject the null hypothesis. so there is enough evidence to conclude that the mean waiting time is less than 3 minutes.