Final answer:
To construct a 90% confidence interval for the mean height of students at GT, find the critical value using the z-table, calculate the standard error, and then use the formula to calculate the lower and upper bounds of the confidence interval.
Step-by-step explanation:
To construct a 90% confidence interval for the mean height of students at GT, we can use the formula:
Lower bound = sample mean - (critical value * standard error)
Upper bound = sample mean + (critical value * standard error)
First, we need to find the critical value. Since the confidence level is 90%, we find the z-score that corresponds to a 5% tail on each side. Using a z-table or calculator, we find that the critical value is approximately 1.645.
The standard error can be calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard deviation is 0.1 feet and the sample size is 21, so the standard error is approximately 0.022.
Plugging in these values, we get:
Lower bound = 5.5 - (1.645 * 0.022) = 5.5 - 0.036
Upper bound = 5.5 + (1.645 * 0.022) = 5.5 + 0.036
Therefore, the 90% confidence interval for the mean height of students at GT is (5.464, 5.536) feet.