Question

Google and Gallup teamed up to survey a random sample of $1673$U.S. students in grades. One of the questions was “How confident are you that you could learn computer science if you wanted to?” Overall, $54\%$of students said they were very confident.

a. Identify the population and the sample.

b. Explain why it was better to randomly select the students rather than putting the survey question on a website and inviting students to answer the question.

c. Do you expect that the percent of all U.S. students in grades 7–12 who would say “very confident” is exactly 54%? Explain your answer.

d. The report also broke the results down by gender. For this question, $62\%$of males and 48% of females said they were very confident. Which of the three estimates $(54\%,62\%,48\%)$do you expect is closest to the value it is trying to estimate? Explain your answer.

Short answer

The answer to these questions is:

a) Because not all samples were possible, it is not a simple random sample.
b) To account for hidden variables, one adult was picked at random.
c) This poll had several gaps in coverage. Those who did not have access to a telephone or who only had access to a cell phone were excluded from the study.
d) The survey results may not accurately reflect the views of the entire population.

Step-by-step solution

Part (a) Step 1: Given information

We have to identify the population and the sample.

Part (a) Step 2: Explanation

Because not all samples were possible, it is not a simple random sample. Given their strategy, they couldn't have gotten all of the responders from the East Coast, for example.

Part (b) Step 1: Given information

We have to tell why it was better to randomly select the students rather than putting the

survey question on a website.

Part (b) Step 2: Explanation

To account for hidden variables, one adult was picked at random. Perhaps those who frequently answer the phone have a different perspective than those who do not frequently answer the phone.

Part (c) Step 1: Given information

We have to tell who would say “very confident” is exactly 54%

Part (c) Step 2: Explanation

There was under-coverage in this survey. Those who do not have telephones and those who have only cell phones were not part of the sampling frame, so their opinions were not measured. Since cell-honeonly users tend to be younger, the results of the survey may not accurately reflect the entire population’s opinions.

Part (c) Step 1: Given information

We have to tell about Which of the three estimates(54%, 62%, 48%) do you expect is closest to the value it is trying to estimate.

Part (d) Step 2: Explanation

There was under-coverage in this survey. Those who do not have telephones and those who have only cell phones were not part of the sampling frame, so their opinions were not measured. Since cell-honeonly users tend to be younger, the results of the survey may not accurately reflect the entire population’s \sopinions.