8. [12 marks] Studies have shown that the amount of time that Canadian adults spend streaming movies is normally distributed with a mean of 12.2 hours per week, and a standard deviation of 4.2 hours per week. A. [4] What percent of Canadians stream movies for more than 18 hours per week? B. [4] If 10 Canadian adults were randomly selected, what is the probability that their average streaming times exceeds 16.5 hours? C. [4] A random sample of 60 Carleton students revealed that the sample mean of the number of hours weekly they streamed movies was 18.0 with a sample standard deviation of 4.6. Test the hypothesis at a 5% level of significance that the mean number of hours Carleton students is different from the national average (12.2 hours per week).
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The amount of time Americans spend watching television is closely monitored by firms such as $\mathrm{AC}$ Nielsen because this helps determine advertising pricing for commercials. (a) Do you think the variable "weekly time spent watching television" would be normally distributed? If not, what shape would you expect the variable to have? (b) According to the American Time Use Survey, adult Americans spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent watching television on a weekday" is 1.93 hours. If a random sample of 40 adult Americans is obtained, describe the sampling distribution of $\bar{x},$ the mean amount of time spent watching television on a weekday. (c) Determine the probability that a random sample of 40 adult Americans results in a mean time watching television on a weekday of between 2 and 3 hours. (d) One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 35 individuals who consider themselves to be avid Internet users results in a mean time of 1.89 hours watching television on a weekday. Determine the likelihood of obtaining a sample mean of 1.89 hours or less from a population whose mean is presumed to be 2.35 hours. Based on the result obtained, do you think avid Internet users watch less television?
Sampling Distributions
Distribution of the Sample Mean
The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours What is the probability that a randomly selected North American adult watches television for more than 7 hours per day? b. What is the probability that the average time watching television by a random sample of five North American adults is more than 7 hours? c. What is the probability, that in a random sample of five North American adults, all five watch television for more than 7 hours per day?
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3. In order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours with a standard deviation of 3.2 hours watching TV per week. a. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. b. Assume that a sample of 62 students was selected that resulted in the same mean and standard deviation. Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week. Please show all workings step by step.
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