Suppose that 50% of the subscribers of a cable television company watch the shop
ID: 3160574 • Letter: S
Question
Suppose that 50% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep shopping channel if the sample proportion is greater than 0.57. What is the approximate probability that the cable company will keep the shopping channel even though the true proportion is only 0.50? Suppose that 50% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep shopping channel if the sample proportion is greater than 0.57. What is the approximate probability that the cable company will keep the shopping channel even though the true proportion is only 0.50?Explanation / Answer
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.57
u = mean = p = 0.5
s = standard deviation = sqrt(p(1-p)/n) = 0.05
Thus,
z = (x - u) / s = 1.4
Thus, using a table/technology, the right tailed area of this is
P(z > 1.4 ) = 0.080756659 [ANSWER]
Related Questions
Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.