Assignments

1. The following hypotheses are given.

*H*_{0}: π = .40

*H*_{1}: π ≠ .40

A sample of 120 observations revealed that *p* = .30. At the .05 significance level, can the null hypothesis be rejected?

a. State the decision rule.

b. Compute the value of the test statistic.

c. What is your decision regarding the null hypothesis?

For the following Problems, use the 6 step hypothesis testing

2. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?

3. 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 .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

4. The null and alternate hypotheses are:

*H*_{0}: π_{1} = π_{2}

*H*_{1}: π_{1} ≠ π_{2}

A sample of 200 observations from the first population indicated that *x*_{1} is 170. A sample of 150 observations from the second population revealed *x*_{2} to be 110. Use the .05 significance level to test the hypothesis.

a. State the decision rule.

b. Compute the pooled proportion.

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis?

5. The null and alternate hypotheses are:

*H*_{0}: μ_{1} = μ_{2}

*H*_{1}: μ_{1} ≠ μ_{2}

A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means?

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