The Graduate Management Admission Test (GMAT) is a test required for admission i

Question

The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Suppose a random sample of 8 students took the test, and their scores were: 699, 560, 414, 570, 521, 663, 727, 413

             a)      Find a point estimate of the population mean.

b)      Write a sentence about how you can verify the data could come from a population that is normally distributed, using the graph below.

c)      Construct and interpret a 95% confidence interval for the true mean score for the population.

d)      How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?

e)      How many students should be surveyed to estimate the mean score within 25 points with 95% confidence?

GMAT 650 550 450 0,5 n 0.976 Normal Quantile

Explanation / Answer

a) from above

hence point estimate of mean =570.875

b) as all the values are approximately equally distributed on Q plot we can assume that data is normally distributed

c) here for (n-1=7) degree of freedom ; at 95 %, t= 2.365

hence confidence interval =sample mean +/- t*std error =470.245 ; 671.505

this interval gives 95% probability to contain true population mean of distribution

d)here std deviation =120.368

for 90% CI, z=1.64485

and margin of error E=25

hence sample size n=(z*std deviation/E)2 =~63

e)for 95% CI, z=1.96

sample size =~90

f) for 99% CI, z=2.5758

sample size n~154

X 699.000 560.000 414.000 570.000 521.000 663.000 727.000 413.000 mean(X) 570.875 std deviation(S) 120.368 std error =S/(n)1/2 42.556

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