# Students t test

1. Based on the specific question under study, how can one always determine which is the null hypothesis (H0) and which is the alternative hypothesis (H1).

2. A consumer advocate tests the claim that the Toyota Corolla actually delivers less than 32 mpg (as stated on the advertisements). So, we have:

H1 : µ < 32 (claim)

H0 : µ > 32

State what the Type I and Type II errors would be in this claim as they relate to Toyota and the consumer.

3. When conducting a hypothesis test, the significance level (?) is chosen by the researcher. Changing ? from 0.05 to 0.10 (or vice versa) could change the entire outcome of the test. What are some reasons, then, why the p-value method of hypothesis testing is considered better than the 5-step method?

4 . A sample of 81 observations is taken from a normal population. The sample mean is 40, and the sample standard deviation is 5. Determine the 95 percent confidence interval for the population mean.

5. Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in downtown Toledo, Ohio. They are considering jointly offering child care for their employees. As apart of the feasibility study, they wish to estimate the mean weekly child-care cost of their employees. A sample of 10 employees who use child care reveals the following amounts spent last week.

$107 $92 $97 $95 $105 $101 $91 $99 $95 $104

Develop a 90 percent confidence interval for the population mean. Interpret the result.

6. The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes traveled.

29 38 38 33 38 21 45 34

40 37 37 42 30 29 35

Develop a 98 percent confidence interval for the population mean. Interpret the result.

7. 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. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?

8.The MacBurger restaurant chain claims that the waiting time of customers for service is

normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The

quality-assurance department found in a sample of 50 customers at the Warren Road

MacBurger 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?

#### Solution Summary

The solution gives complete steps of students t test for comparing the population mean. Null hypothesis, alternative hypothesis, critical value, P value, student t statistic are given. Interpretation of the results are also given.