Question

The amount of time Americans spend watching television is closely monitored by firms such as A.C. Nielsen because this helps to determine the advertising pricing for commercials. According to a recent survey, adult Americans spend an average of 2.34 hours per day watching television on a weekday. Assume the standard deviation for "time spent watching television on a weekday" is 1.91 hours.

A) If a random sample of 60 adult Americans is obtained, what is the probability that the sample mean time watching television is between 2 and 3 hours?

B) One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 40 individuals who consider themselves to be avid Internet users results in a mean time of 1.75 hours watching television on a weekday. Determine the likelihood of obtaining a sample mean of 1.75 hours or less from a population who mean is presumed to be 2.34 hours.

C) Based on your probability obtained in part B), do you think avid Internet users watch less television? Yes, I believe they watch TV less than 2.34 hours on average, because this is not a small probability Yes, I believe they watch TV less than 2.34 hours on average, because this is a very small probability No, I believe they watch TV less than 2.34 hours on average, because this is not a small probability No, I believe they watch TV less than 2.34 hours on average, because this is a very small probability

Answer 1

Solution:

A) If a random sample of 60 adult Americans is obtained, what is the probability that the sample mean time watching television is between 2 and 3 hours?

Answer: It is required to find:

Using the z-score formula, we have;

Now using the standard normal table, we have:

Therefore, the probability that the sample mean time watching television is between 2 and 3 hours is 0.9123

B) One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 40 individuals who consider themselves to be avid Internet users results in a mean time of 1.75 hours watching television on a weekday. Determine the likelihood of obtaining a sample mean of 1.75 hours or less from a population that mean is presumed to be 2.34 hours.

Answer: We are required to find:

Now using the standard normal table, we have:

Therefore, the likelihood of obtaining a sample mean of 1.75 hours or less is 0.0254

C) Based on your probability obtained in part B), do you think avid Internet users watch less television?

Answer: Yes, I believe they watch TV less than 2.34 hours on average, because this is a very small probability