Question

Long Answer Questions 3. A random sample of Math SAT Scores of 20 applicants to the Isenberg School of Management are reported with a mean of 510 and a variance of 930. Assume that the Math SAT scores for Isenberg applicants are normally distributed - a) Construct a 90% confidence interval for the sample. b) Interpret your answer to part a. Put your answer to part a into context of the actual question c) If we changed it to a 98% confidence level, what would the margin of error be? (2 decimal places) d) ***This part is not related to part C. Now assume that we know that the population standard deviation is 50. If we wanted a 98% confidence level and the margin of error to be 10, how big of a sample of Isenberg applicants would we need to look at?

Answer 1

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Answer:

a)

Confidence interval would be 510 ±1.729√(930/20) 1.729 comes from t table with degrees of freedom 20-1=19.

510±2.6367 (507.36, 512.63)

b)

The interpretation is that we can be 90% confident (9 times out of ten) that the true mean of the population (applicants to the school) will be in this interval.(507.36, 512.63)

c)

At a 98% CI the margin of error would be 2.539√930/20= 3.87

d)

If we wanted a margin of error of 3.87, we would have

n= (2.326* sqrt(930)/3.87)^2= 335.95 round to 336 people. sqrt(930) is the standard deviation which is the square root of the variance.