RESEARCH METHODOLOGY

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STATISTICAL TECHNIQUES AND TOOLS

CONFIDENCE INTERVALS

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A random sample of 42 textbooks has a mean price of $114.50 and a standard deviation of $12.30. Find a point estimate for the mean price of all textbooks.
A
$42
B
$12.30
C
$114.50
D
$2.73
Explanation: 

Detailed explanation-1: -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-2: -Lower limit = x̄-E = 15.125-0.477 = 15.21 (rounded to two decimal places) Upper limit = x̄ + E = 15.125 + 0.477 = 15.79 (rounded to two decimal places) The 98% confidence interval for the mean amount of juice in all such bottles is 15.21 to 15.79 ounces.

Detailed explanation-3: -When you use a standard normal distribution (aka Gaussian Distribution): About 68% of values fall within one standard deviation of the mean. About 95% of the values fall within two standard deviations from the mean.

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