# Solutions for Hypothesis Testing

1. In Meijer supermarket, the customer's waiting time to check out is approximately normally distributed with a standard deviation of 2.5 minutes. A sample of 25 customer waiting times produced a mean of 8.2 minutes. Is this evidence sufficient to reject the supermarket's claim that its customer checkout time averages no more than 7 minutes? Complete this hypothesis test using the 0.02 level of significance.

Solve using the classical approach.

Your answer:

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

2. Which of the following would be the correct hypotheses for testing the claim that the mean lifetime of a cellular phone battery, while the phone is left on, is less than 24 hours?

A) Ho: :u = 24, Ha: u; does not equal; 24

B) Ho: :u = 24(>=), Ha: u < 24

C) Ho: :u = 24(=<), Ha: u > 24

D) Ho: :u > 24, Ha: u =< 24

3. An automobile manufacturer wants to estimate the mean gasoline mileage that its customers will obtain with its new compact model. How many sample runs must be performed in order that the estimate be accurate to within 0.25 mpg at 90% confidence? (Assume that sigma = 2.0.)

4. Assume that z is the test statistic and calculate the value of z*; for testing the null hypothesis Ho: u =150.0 when sigma = 4.5, n=15, x(bar)=147.8

5. A statistician was testing the following hypotheses:

Ho:u = 500 vs. Ha: u does not equal 500.

The p-value approach was to be used. A sample of size 49 gave a sample mean of 508. Given that sigma = 30 2, and alpha = 0.01, find the p-value, and write your conclusion.

6. Which of the following is the probability of making a Type I error?

A) alpha

B) 1 - alpha

C) beta

D) 1 - beta

#### Solution Preview

1. In Meijer supermarket, the customer's waiting time to check out is approximately normally distributed with a standard deviation of 2.5 minutes. A sample of 25 customer waiting times produced a mean of 8.2 minutes. Is this evidence sufficient to reject the supermarket's claim that its customer checkout time averages no more than 7 minutes? Complete this hypothesis test using the 0.02 level of significance.

Solve using the classical approach.

Your answer:

Step 1: The null hypothesis (H0) and the alternative hypothesis (H1)

H0: mu<=7

H1: mu>7

Step 2: Select a significance level alpha.

We choose alpha=0.02

Step 3: Calculate a statistic.

Given xbar=8.2, sigma=2.5, n=25. We can compute the test z-statistic as follows.

z=(xbar-7)/sigma*sqrt(n)

...

#### Solution Summary

This solution answer various hypothesis testing questions.