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.
<h3>What is the margin of error in statistics?</h3>
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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