Question on Confidence Interval and 95%

In summary, a study was conducted by MBA student Daniel R. Dalach where a sample of 20 pages was taken from the Ameritech Pages Plus Yellow Pages, a 1,591-page phone directory. The mean area devoted to display ads on each page was measured in square millimeters, with data ranging from 0 to 536. The questions to answer are: (a) the construction of a 95 percent confidence interval for the true mean, (b) the potential issue of normality, (c) the necessary sample size to obtain an error of ±10 square millimeters with 99 percent confidence, and (d) a more reasonable requirement if the previous one is not feasible.
  • #1
das4862
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A sample of 20 pages was taken without replacement from the 1,591-page phone directory
Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured(a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:

0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130

Questions to answer are:

(a) Construct a 95 percent confidence interval for the true mean. (b) Why might normality be an
issue here? (c) What sample size would be needed to obtain an error of ±10 square millimeters
with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is. (Data
are from a project by MBA student Daniel R. Dalach.) DisplayAds
 
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What have you tried for these?
 

What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. It is often used in statistical analysis to estimate the true value of a population based on a sample of data.

Why is a 95% confidence interval commonly used?

A 95% confidence interval is commonly used because it is a standard level of confidence that provides a good balance between precision and reliability. It means that there is a 95% chance that the true population parameter falls within the calculated interval.

How is a confidence interval calculated?

A confidence interval is calculated using a formula that takes into account the sample size, sample mean, and standard deviation. The most common formula is the standard error formula, which multiplies the standard deviation by the appropriate critical value based on the desired confidence level.

What does a larger confidence interval indicate?

A larger confidence interval indicates that there is more uncertainty in the estimate of the true population parameter. This could be due to a smaller sample size, a wider range of data, or a lower level of confidence.

Can confidence intervals be used to make predictions?

No, confidence intervals should not be used for making predictions. They are used to estimate the true value of a population parameter based on a sample, but they do not take into account any future data or changes in the population.

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