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# Six hypothesis testing problems

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1.) In a normal distribution with mean 59 and standard deviation 22, how large a sample must be taken so that there will be at least a 90 percent chance that its mean is greater than 53?

2.) In the second week of June 1996, the average number of units produced per week for all models of automobiles manufactured in the U.S. was 2,221. A sample of manufacturers' planned production in the second week of June 1997 was as follows:

Model Camaro Sunbird Century Topaz Lynx Voyager LeBaron
Units 5,004 2,931 3,773 1,313 1,292 3,600 2,600

Do these data indicate that planned production in the third week of June 1997 was significantly different from actual production in the previous year? Use the 0.05 level of significance.

3.) A sample of 20-year conventional mortgage rates at 11 randomly chosen banks in New York yielded a mean rate of 7.50 percent and a standard deviation of 0.40 percent. A similar sample taken at 9 randomly chosen banks in Nebraska had a mean rate of 7.75 percent, with a standard deviation of 0.30 percent. Do these samples provide evidence to conclude (at 0.10 level of significance) that conventional mortgage rates in New York and Nebraska come from population with different means?

4.) The Coke Institute has claimed that at least 45 percent of American children regularly have a can of Coke with their dinner. A random sample of 450 individuals revealed that 225 of them were regular Coke drinkers at dinner. What is the prob value for a test of hypotheses seeking to show that the Coke Institute's claim was correct? (Hint: Test Ho: p= 0.45, versus H1: p> 0.45).

5.) If a sample of 30 observations reveals a sample mean of 55 and a sample variance of 4.0, test the hypothesis that the population mean is 65, against the alternative that it is some other value. Use the 0.05 significance level.

6.) In September 2000, a survey of 110 economists found that 84 who believed that the recession had already ended. A survey of 140 purchasing agents found 86 who believed the recession had ended. At a 0.05 level of significance, should you conclude that the economists were more optimistic about the economy than the purchasing agents?

Text Book: Statistics for Management (7th ed).

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#### Solution Summary

Solutions to six separate problems (see the following):

1. Sample size calculation when estimating the mean of a normal distribution
2. Small sample hypothesis test for a population mean
3. Small sample hypothesis test for the difference of two population means
4. Hypothesis test for a population proportion
5. Small sample hypothesis test for a population mean
6. Hypothesis test for a population proportion.

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