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Question 3 To track changes over...

Question 3

To track changes over time in the quality of education offered by primary and

secondary schools in the U.S., an outfit called the National Assessment of

Educational Progress (NAEP) administers tests each year in a variety of

subjects to nationwide random samples of students. They actually use cluster

sampling rather than simple random sampling, but their method is roughly

equivalent to taking an SRS of about 950 students from the population of all

U.S. students in a given grade in any given year.

In 1975 the NAEP gave a math test to 17-year-olds. One of the items on the

test was as follows:

Do the following addition: 1/2 + 1/3 = ...

617 of the 950 students knew the right answer, 5/6 (the other popular

response was 2/5).

Estimate p, the percentage of all 17-year-old students in the U.S. who knew

the right answer, attach a give-or-take to your estimate, and construct a 95%

confidence interval for p.

If they wanted to be 95% sure of getting the national percentage p right to

within 2 percentage points, how many students should they have sampled?

To track changes over time in the quality of education offered by primary and

secondary schools in the U.S., an outfit called the National Assessment of

Educational Progress (NAEP) administers tests each year in a variety of

subjects to nationwide random samples of students. They actually use cluster

sampling rather than simple random sampling, but their method is roughly

equivalent to taking an SRS of about 950 students from the population of all

U.S. students in a given grade in any given year.

In 1975 the NAEP gave a math test to 17-year-olds. One of the items on the

test was as follows:

Do the following addition: 1/2 + 1/3 = ...

617 of the 950 students knew the right answer, 5/6 (the other popular

response was 2/5).

Estimate p, the percentage of all 17-year-old students in the U.S. who knew

the right answer, attach a give-or-take to your estimate, and construct a 95%

confidence interval for p.

If they wanted to be 95% sure of getting the national percentage p right to

within 2 percentage points, how many students should they have sampled?

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