Question

The National Collegiate Athletic Association (NCAA) requires Division II athletes to score at least 820 on the combined mathematics and reading parts of the SAT in order to compete in their first college year. The scores of the 1.5 million high school seniors taking the SAT last year are approximately Normal with mean 1026 and standard deviation 209. For an SRS size 200

1) Find the mean and standard deviation of x bar

2) What is the distribution of x bar?

3) What is the probability that a sample mean value exceeds 1028?

4) The highest 2.5% of sample mean value are higher than ____

5) Has the average score increased since last year? To answer this, do the followings:

I. A SRS size 200 gives a sample mean of 1028. State hypotheses, find the test statistic, pvalue, and express your conclusion using a significance level of α=2.5%.

a. Hypotheses (Use notations)

b. test statistic

c. pvalue

d. Conclusion? Include practical terms.

II. Find a 95% confidence interval for the mean SAT score.

Answer 1

Let denotes the mean score for an SRS of size 200.

1) The mean of = 1026

The standard deviation of =

2) - 3)

4)

5) Let denotes the average SAT score this year.

Conclusion : There is not sufficient evidence to conclude that the average score has increased since last year.

6)