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# Sampling and hypothesis testing

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1) A woman and her son are debating about the average length of a preacher's sermons on Sunday morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes. For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05 level of significance, he wishes to determine whether he is correct in thinking that the average length of sermons is more than 20 minutes. What is the test statistic?

2) In developing the Edsel in the 1960s, the Ford Motor Company had two samples in different geographic areas taken to determine what consumers wanted in a midsize luxury car. History tells us that the Edsel was a marketing and financial disaster. One of the Ford Motor Company's mistakes was in not taking a representative sample. How could a company today avoid Ford's mistake?
a. By taking a stratified random sample from across the country
b. By using a judgment sample to be sure and include the correct respondents
c. By taking a quota sample of owners of all domestic cars

3) Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume that the standard deviation = \$0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within \$0.25 of the true mean ticket prices?

4) In a given year, the average annual salary of an NFL football player was \$189,000, with a standard deviation of \$20,500. If a sample of 50 players was taken, what is the probability that the sample mean will be \$192,000 or more?

5) An executive working for a fast food restaurant corporation believes a street located near a major highway interchange might be a profitable location. A random sample of sixty days is taken to estimate the average cars per day passing by the location. Based on the sample date, the executive concludes that the average isn't high enough to yield a profitable outlet. Six months later, a competitor builds at the same location and reports it to be one of its most profitable new stores. What type of error was made by the executive?
a. Null hypothesis
b. Alternative hypothesis
c. Type I
d. Type II

6) Suppose an actual census showed that 18.4% of the households in California have incomes in excess of \$50,000. What is the probability that the sample proportion will be 0.22 or greater for a random sample of 750 households from a city population that totals 10,000?

7) A manufacturer of light bulbs wishes to determine the life of her 200 watt bulbs. Because she is concerned about __________, she decides to test only a sample of all the 200 watt bulbs.
a. unknown parameters
b. nonsampling error
c. destructive sampling

8) A human resource manager wants to determine a confidence interval estimate for the mean test score for the next office-skills test to be given to a group of job applicants. In the past, the test scores have been normally distributed with a mean of 74.2 and a standard deviation of 30.9. Determine a 95% confidence interval estimate if there are 30 applicants in the group.

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#### Solution Summary

Answers questions on sampling and hypothesis testing: test statistic, stratified random sample, judgment sample, sample size, type of error, probability, proportion, confidence interval etc.

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