Question

The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores on the quantitative portion of the GRE follow a normal distribution with standard deviation of 8.8. Suppose a random sample of 10 students took the test, and their scores are given below:

152, 126, 146, 149, 152, 164, 139, 134, 145, 136  

1. Find a point estimate of the population mean. The point estimate for the population mean is 144.3.
2. Construct a 95% confidence interval for the true mean score for this population.
3. How many students should be surveyed to estimate the mean score within 3 points with 95% confidence?
4. How many students should be surveyed to estimate the mean score within 1 point with 95% confidence?
5. How many students should be surveyed to estimate the mean score within 0.5 points with 95% confidence?

PLEASE TYPE DONT WRITE THANK YOU!!

Answer 1

(a)

A point estimate of the population mean = 1443/10 = 144.3

(b)

SE = /

= 8.8/

= 2.7828

= 0.05

ndf = 10 - 1 = 9

From Table, critical values of t = 2.2622

Confidence Interval:

144.3 (2.2622 X 2.7828)

= 144.3 6.2953

= (138.0047 ,150.5953)

Confidence Interval:

138.0047 <       <   150.5953

(c)

Number of students (n) is given by:

Given:

= 0.05

From Table, critical values of Z = 1.96

= 8.8

e = 3

Substituting, we get:

So,

Answer is:

34

(d)

Given:

= 0.05

From Table, critical values of Z = 1.96

= 8.8

e = 1

Substituting, we get:

So,

Answer is:

298

(e)

Given:

= 0.05

From Table, critical values of Z = 1.96

= 8.8

e = 0.5

Substituting, we get:

So,

Answer is:

1190