Question

In: Statistics and Probability

The mean and standard deviation of a random sample of n measurements are equal to 33.5...

The mean and standard deviation of a random sample of n measurements are equal to 33.5 and 3.5, respectively.

a. Find a 90% confidence interval for m if n = 144.

b. Find a 90% confidence interval for m if n = 576.

c. Find the widths of the confidence intervals found in parts a and b.

What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

Expert Solution

a. Find a 90% confidence interval for m if n = 144.

We need to construct the 90% confidence interval for the population mean . The following information is provided:

Sample Mean	33.5
Population Standard Deviation	3.5
Sample Size	144

The critical value for α = 0.1 is = 1.645 . The corresponding confidence interval is computed as shown below:

CI = (33.02, 33.98)

b. Find a 90% confidence interval for m if n = 576

We need to construct the 90% confidence interval for the population mean . The following information is provided:

Sample Mean	33.5
Population Standard Deviation	3.5
Sample Size	576

The critical value for α = 0.1 is = 1.645 . The corresponding confidence interval is computed as shown below:

CI = (33.26, 33.74)

c. Find the widths of the confidence intervals found in parts a and b.

Width when n = 144

33.98 - 33.02 = 0.96

Width when n = 576

33.74 - 33.26 = 0.48

What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

As the sample size is quadrupeled the width is reduced to half

orchestra answered 1 year ago

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