Question

A random sample of 16 statistics examinations was taken. The average sample score was 76.2 with a sample variance of 144. The 99% confidence interval for the true average examination score is
Select one:

A.
49.677 to 102.723

B.
73.99 to 78.41

C.
67.359 to 85.041

D.
67.437 to 84.963

E.
None of the above answers is correct

Answer 1

99% confidence interval for the population average examination score is between a lower limit of 67.35 and an upper limit of 85.05. The correct option is C.

What is the margin of error in statistics?

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

The interval will be calculated as below:-

Confidence interval = mean +/- margin of error (E)

mean = 76.2

variance = 144

sd = sqrt(variance) = sqrt(144) = 12

n = 16

Degree of freedom (df) = n - 1 = 16- 1 = 15

Confidence level (C) = 99% = 0.99

Significance level = 1 - C = 1 - 0.99 = 0.01 = 1%

t-value corresponding to 15 df and 1% significance level is 2.95

The margin of error will be:-

E = t×sd/√n = 2.95 ×  12/√16 = 8.85

The interval will be:-

Lower limit = mean - E = 76.2 - 8.85 = 67.35

Upper limit = mean + E = 76.2 + 8.85 = 85.05

Therefore, the 99% confidence interval for the population average examination score is between a lower limit of 67.35 and an upper limit of 85.05. The correct option is C.

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