Question

The data set represents the scores of 12 randomly selected students on the SAT Physics Subject...

The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation is 103. (Adapted from The College Board) 670 740 630 620 730 650 720 620 640 500 670 760

(a) Find the point estimate of the population mean.

(b) Construct a 90% confidence interval for the population mean. Interpret the results.

(c) Determine the minimum sample size required to be 95% confident that the sample mean test score is within 10 points of the population mean test score.

Homework Answers

Answer #1

a) Point estimate of the population mean would be simply the mean of the sample data:

=> = 662.5

b) For 90% confidence, critical value of z = 1.64

Hence,

CI = ( ) = (662.5 1.64*103/) = (662.5 48.76) = (613.73, 711.26)

c) 10 points of the population mean test score = 0.1 * 662.5 = 66.25

So we want, 66.25

=> 1.64*103/ 66.25

=> n 6.5

=> n = 7 is the minimum sample size.

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