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Confidence Interval Examples

The critical t* values depend on both the confidence level and the sample size n. The table below is a very simplified critical value table for the t-distribution.

Example 1

The weights of a random sample of 31 male high school students were recorded. The mean weight was 140 pounds and the standard deviation was 20 pounds. Find a 90% confidence interval for the mean weight of all male students at this high school.

Confidence Interval

Using the TI-83

1.697 20 31 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

140 calculates the lower bound of the interval by subtracting the margin of error from the sample mean.

140 calculates the upper bound of the interval by adding the margin of error to the sample mean.

Using Some Other Calculators

1.697 * 20 / 31 sqrt=MS calculates the margin of error and stores it in memory.

140 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample mean.

140 + MR = calculates the upper bound of the interval by adding the margin of error to the sample mean.

 

Example 2

The weights of a random sample of 11 female high school students were recorded. The mean value was 110 pounds and the standard deviation was 17 pounds. Find a 95% confidence interval for the mean weight of all female students at this high school.

Confidence Interval

Using the TI-83

2.228 17 11 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

110 calculates the lower bound of the interval by subtracting the margin of error.

110 calculates the upper bound of the interval by adding the margin of error.

Using Some Other Calculators

2.228 * 17 / 11 sqrt=MS calculates the margin of error and stores it in memory.

110 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample mean.

110 + MR = calculates the upper bound of the interval by adding the margin of error to the sample mean.

 

Example 3

The quality control officer collects a random sample of 51 yardsticks from the day's production run. The sample mean is 36.05 inches and the standard deviation is 0.09 inches. Find a 99% confidence interval for the mean length of all yardsticks made that day.

Confidence Interval

Using the TI-83

2.678 0.09 51 calculates the margin of error and stores it as M (you could use any variable but I chose M for margin of error).

36.05 calculates the lower bound of the interval by subtracting the margin of error.

36.05 calculates the upper bound of the interval by adding the margin of error.

Using Some Other Calculators

2.678 * 0.09 / 51 sqrt=MS calculates the margin of error and stores it in memory.

36.05 - MR = calculates the lower bound of the interval by subtracting the margin of error from the sample mean.

36.05 + MR = calculates the upper bound of the interval by adding the margin of error to the sample mean.