STATISTICAL TECHNIQUES AND TOOLS
CONFIDENCE INTERVALS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.Find the Standard Error to three decimal places.
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0.336
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0.33566
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13.156
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0.087
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Explanation:
Detailed explanation-1: -Calculating a C% confidence interval with the Normal approximation. ˆp±z√ˆp(1−ˆp)n, where the value of z is appropriate for the confidence level. For a 95% confidence interval, we use z=1.96, while for a 90% confidence interval, for example, we use z=1.64.
Detailed explanation-2: -Since 95% of values fall within two standard deviations of the mean according to the 68-95-99.7 Rule, simply add and subtract two standard deviations from the mean in order to obtain the 95% confidence interval.
Detailed explanation-3: -The stated confidence level was 95% with a margin of error of ± 2. We can conclude that the results were calculated to be accurate to within 2 percentages points 95% of the time.
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