In: Statistics and Probability
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?
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