FOR INSTRUCTORS USE
|1. Suppose that a new production method will be
implemented if a hypothesis test supports the conclusion that the new
method reduces the mean operating cost per hour.
|a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.|
|b. What is the Type I error in this situation? What are the consequences of making this error?|
|c. What is the Type II error in this situation?
What are the consequences of making this error?
|a. Determine the number of households that a historian needs from old census records to estimate the mean household size in a region within 0.25 person of the true mean with 99% confidence. An archivist published the standard deviation of household sizes for the nation during the same period as 1.32 persons, and there is no reason to suspect that variation in household size in the region differed from the national value.|
|b. How many bowlers must be randomly interviewed to ascertain all bowlers' interest in a new bowling alley in a town? The prospective investor wishes to be 90% sure the estimate is within 0.02 of the true proportion of level of interest.|
|3. A CNN report in January 1994 claimed that 50% of all roller bladders get injured. A random sample of 849 roller bladders revealed that only 210 of them had been injured.|
|a. Is there statistical evidence at a=0.05 significance level to reject the CNN report's credibility if the purpose of the study was to prove that CNN exaggerated upward the actual injury rate of this recreational activity? Incorporate a statement on the p-value in your conclusion.|
|b. Construct a 90% confidence interval for the true
proportion of injured roller bladders.
|4. Prior to the institution of a new safety program, the average number of on-the-job accidents per day at a factory was 4.5. To determine whether the safety program has been effective in reducing the average number of accidents per day, a random sample of 120 days is taken after the institution of the new safety program, and the number of accidents per day is recorded. The sample mean was 3.7. Assume that the population standard deviation is 2.6.|
|a. Is there sufficient evidence to conclude (at significance level 0.01) that the average number of on-the-job accidents per day at the factory has decreased since the institution of the safety program? claim? State the null and alternative hypotheses, find the p-value and report your conclusion.|
|b. Set up a 99% confidence interval for the average
number of accidents per day after the institution of the safety program.
|5. How do makers of Kleenex know how many tissues to put in a box? According to the Wall street Journal (1984), the marketing experts at Kimberly-Clark Corporation have "little doubt that the company should put 60 tissues in each pack." The researchers determined that 60 is "the average number of times people blow their nose during a cold" by asking hundreds of customers to keep count of their Kleenex use in diaries. Suppose that for a random sample of 19 Kleenex users mean was 57 and standard deviation was 26.|
|a. Is this sufficient evidence to dispute the researchers' claim? State the null and alternative hypotheses, find the p-value and report your conclusion. Use a=0.05.|
|b. Construct a 95% confidence interval for the average number times Kleenex users blow their nose during a cold.|
|c. What assumptions are necessary to ensure the
validity of your answers to a and b?