The heights of a random sample of 50 college students showed a sample mean of 174.5 centimeters and a sample standard deviation of 6.9 centimeters. Construct a 98% confidence interval for the mean height of all college students.

Step-by-step explanation:

We want to construct a 98% confidence interval for the mean height of all college students.

Number of sample, n = 450

Mean, u = 174.5 centimeters

Standard deviation, s = 6.9 centimeters

For a confidence level of 98%, the corresponding z value is 2.33. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z * standard deviation/√n

It becomes

174.5 ± 2.33 * 6.9/√450

= 174.5 ± 2.33 * 0.325

= 174.5 ± 0.757

The lower end of the confidence interval is 174.5 - 0.757 = 173.743

The upper end of the confidence interval is 174.5 + 0.757 = 175.257

Therefore, with 98% confidence interval, the mean height of all college students is between 173.743 centimeters and 175.257 centimeters.