Question

A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured in square millimeters (mm2). The sample mean is 346.5 mm2 and sample standard deviation is 170.38 mm2. The 95 percent confidence interval for the mean is:

Answer 1

The 95 percent confidence interval for the mean is (266.76,426.24).

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

The formula of Confidence Interval =  Mean ±   $t\frac{Standard Deviation}{\sqrt{number of observations} }$

where t is a constant

Given:

Mean = 346.5

Standard Deviation = 170.378

t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093

∴ Substituting values in formula we get

E = $2.093 X170.378/\sqrt{20}$ = 2.0931.96 x 38.0976=79.74

95% Confidence interval : (346.5-79.74,346.5+79.74)

95% Confidence interval : (266.76,426.24)

Learn more about confidence intervals here :

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