Question

According to a survey, 64% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the Internet. Suppose a random sample of 300 Americans from this age group is selected. Complete parts (a) through (d) below.

a. What percentage of the sample would we expect to watch television primarily through streaming services?
b. Verify that the conditions for the Central Limit Theorem are met.
The Random and Independent condition, The Large Samples condition, and The Big Populations condition can reasonably be assumed to hold.
c. Would it be surprising to find that 199 people in the sample watched television primarily through streaming services? Why or why not? Select the correct choice below and fill in the answer box within your choice. (Type an integer or decimal rounded to two decimal places as needed.)

Answer 1

64% of the sample is expected to watch television primarily through streaming services. The conditions for the Central Limit Theorem are met. It would be somewhat surprising to find that 199 people in the sample watched television primarily through streaming services.

Step-by-step explanation:

To answer part (a), since 64% of young Americans aged 18 to 29 say they watch television primarily through streaming services, we can expect that 64% of our sample will also watch television primarily through streaming services. So, 64% of 300 is 192. Therefore, we expect that about 192 people in the sample will watch television primarily through streaming services.

In part (b), the conditions for the Central Limit Theorem are met. The Random and Independent condition is satisfied since the sample is randomly selected and the individuals' choices regarding streaming services are independent. The Large Samples condition is satisfied since the sample size of 300 is greater than 30. The Big Populations condition is satisfied since the survey is conducted on young Americans aged 18 to 29, which is a subpopulation of the larger population of young Americans.

For part (c), if 199 people in the sample watched television primarily through streaming services, it would be somewhat surprising but not extremely unlikely. Since the expected value is 192, it falls within a reasonable range of values. However, it is still on the higher side of the range, so it might be a bit unexpected.