Paying for music downloads. A survey of Canadian teens aged 12 to 17 years repor

Question

Paying for music downloads. A survey of Canadian teens aged 12 to 17 years reported that roughly 75% of them used a fee-based website to download music. You decide to interview a random sample of 15 U.S. teenagers. For now, assume that they behave similarly to the Canadian teenagers. What is the distribution of the number X who used a fee-based website to download What is the probability that at least 12 of the 15 teenagers in your sample used a fee- based website to download music. Paying for music downloads, continued. Refer to Exercise 5.52. Suppose that only 60% of the U.S. teenagers used a fee-based website to download music. If you interview 15 U.S. teenagers at random, what is the mean of the count X who used a fee-based website to download music? What is the mean of the proportion who used a fee-based website to download music? in your sample Repeat the calculations in part (a) for samples of size 150 and 1500. What happens to the mean count of successes as the sample size increases? More on paying for music downloads. Consider the settings of Exercises 5.52and 5.54. Using the 75% rate of the Canadian teenagers, what is the smallest number m out of n = 15 U.S. teenagers such that P(X lessthanorequalto m) is no larger than 0.05? You might consider m or fewer students as evidence that the rate in your sample is lower than the 75% rate of the Canadian teenagers. Now using the 60% rate of the U.S. teenagers and your answer to part (a), what is P(X lessthanorequalto m)? This represents the chance of obtaining enough evidence given that the rate is 60%. If you were to increase the sample size from n = 15 to n = 100 and repeat parts (a) and(b), would you expect the probability in (b) to increase or decrease? Explain your answer.

Explanation / Answer

Solution for 55.5 as specified in the request

Let X = number of US teenagers who pay for music downloads. Then, X ~ Binomial with parameters

n = sample size and p = proportion rate of teenagers who pay for music downloads.

Part (a)

Here n = 15, p = 0.75 and we want m such that P(X m) 0.05.

Using Excel Function, m is found to be 7 ANSWER

[P(X 7) = 0.0173 and P(X 8) = 0.0562]

Part (b)

Here we have n = 15, p = 0.6 and m = 7 and we want P(X m).

Again, using Excel Function, this probability is found to be 0.2131 ANSWER

Part (c)

Here we have n = 100 p = 0.75 and we want m such that P(X m) 0.05.

Using Excel Function, m is found to be 67 ANSWER 1

[P(X 67) = 0.0446 and P(X 68) = 0.0693]

And P(X 67/given p = 0.6) = 0.9385 ANSWER 2

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