1 . Suppose that the population of the scores of all high school seniors that to

Question

1. Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a Normal distribution, with mean and standard deviation = 100. You read a report that says, “On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for is 512.00 ± 25.76.” The confidence level for this interval is:

a. 90%.
b. 99%.
c. > 99.9%.

2. Twenty-five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores to be used in a study. These 25 seniors had a mean Math SAT score of = 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is = 100. Assuming the population of Math SAT scores for seniors in the district is approximately Normally distributed, a 90% confidence interval for the mean Math SAT score for the population of seniors computed from these data is:

a. 450 ± 39.2.
b. 450 ± 164.5.
c. not trustworthy.

3. If I wanted the margin of error for the 95% confidence interval to be 1 inch, I should select a simple random sample of size: (assume the population standard deviation = 2.415)

a. 7.
b. 23.
c. 39.

Explanation / Answer

Solution:-

1) option B. 99%

=> ME = z*sd/sqrt(n)

25.76 =z*100/sqrt(100)

25.76 = z*10

z=2.576

b) option  b. 450 ± 164.5.

90% confidence interval : X +/- Z *s/sqrt(n) = 450 +/- 1.645*100 = 450 ± 164.5

c) option a. 7

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