The sponsors of television shows targeted at the children’s market wanted to know the amount of time children spend watching television because the types and number of programs and commercials are greatly influenced by this information. As a result, it was decided to survey 100 North American children and ask them to keep track of the number of hours of television they watch each week. From past experience, it is known that the population standard deviation of the weekly amount of television watched is σ = 8.0 hours. The television sponsors want an estimate of the amount of television watched by the average North American child. A confidence level of 95% is judged to be appropriate.
Answer to relevant QuestionsReview Exercise 10.41. Describe what happens to the sample size whena. The population standard deviation increases.b. The confidence level increases.c. The bound on the error of estimation increases.a. A statistics practitioner would like to estimate a population mean to within 10 units. The confidence level has been set at 95% and σ = 200. Determine the sample size.b. Suppose that the sample mean was calculated as ...a. The mean of a sample of 25 was calculated as x̄ = 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence.b. Repeat part (a) changing the ...H0: µ = 1000H1: µ ≠ 1000σ = 200, n = 100, x̄ = 980, α = .01Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution.Find the probability of a Type II error for the following test of hypothesis, given that µ = 1,050.H0: µ = 1,000H1: µ > 1,000α = .01, σ = 50, n = 25
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