basic review problems - STAT 5333 Inference One and Two...

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STAT 5333 Inference One and Two Sample Questions FALL 2016 1. A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. The standard deviation of the population is $5230. (a) At 𝛼 = 0.05, test the claim that assistant professors earn more than $42,000 a year. (b) Find a 99% confidence interval for the mean salary of assistant professors. 2. A researcher claims that the average cost of men’s athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following costs (in dollars). (The costs have been rounded to the nearest dollar.) 60 70 75 55 80 55 50 40 80 70 50 95 120 90 75 85 80 60 110 65 80 85 85 45 75 60 90 90 60 95 110 85 45 90 70 70 (a) Is there enough evidence to support the researcher’s claim at 𝛼 = 0.10? (b) Find a 90% confidence interval for mean price. 3. The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects a random sample of 35 stroke victims at the hospital and finds that the average cost of their rehabilitation is $25,226. The standard deviation of the population is $3251. At 𝛼 = 0.01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different from $24,672?
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4. A researcher wishes to test the claim that the average of lifeguards in Ocean City is greater than 24 years. She selects a sample of 26 guards and finds the mean of the sample to be 24.7 years, with a standard deviation of 2 years. Is there evidence to support the claim at 𝛼 = 0.05? Use the P-value method.
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