Chapter 4, Problem T4.13SPT

(a)

To determine

To identify the population and the sample.

Answer to Problem T4.13SPT

Population: all US students in grades $7-12$

Samples: The $1673$ US students in grades $7-12$ surveyed.

Explanation of Solution

The population is the area we want to study about and the sample is a small subgroup of the population that represent the population as a whole.

Thus, population: all US students in grades $7-12$

And samples: The $1673$ US students in grades $7-12$ surveyed.

(b)

To determine

To explain why it is better to randomly select the students rather than putting the survey question on website and inviting students to answer the question.

Explanation of Solution

It is better to randomly selecting the students rather than putting the survey question on website and inviting students to answer the question because random selection reduces the effects of bias due to self-selection and also allows the results to be inferred to a larger population. In this case, students who respond to an online survey might be more interested in computer science, leading to an estimate that is too high.

(c)

To determine

To explain do you expect that the percentage of all U.S. students in grade $7-12$ who would say “very confident” is exactly $54\%$ or not.

Answer to Problem T4.13SPT

No.

Explanation of Solution

We do not expect that the percentage of all U.S. students in grade $7-12$ who would say “very confident” is exactly $54\%$ because of sampling variability as sampling variability is how much an estimate varies between samples. “Variability” is another name for range; Variability between samples indicates the range of values differs between samples.

(d)

To determine

To explain which of the three estimates $(54\%,62\%,48\%)$ do you expect closest to the value it is trying to estimate.

Answer to Problem T4.13SPT

  $54\%$ .

Explanation of Solution

The estimate of $54\%$ , we expect closest to the value it is trying to estimatebecause it was based on a sample size of sizes. Larger sample sizes should yield results that are closer to the truth about the population.