Question

. We have IQ test scores of 31 seventh-grade girls in a Midwest school district. We have calculated that sample mean is 105.84 and the standard deviation is 14.27. a. Give a 99% confidence interval for the average score in the population. What is the margin of error?

Answer 1

Answer 2

To calculate a 99% confidence interval for the average score in the population, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value is obtained from the t-distribution based on the desired confidence level and the degrees of freedom. Since the sample size is 31, the degrees of freedom are 31 - 1 = 30.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard error = standard deviation / √(sample size)

Substituting the given values:

Sample mean = 105.84 Standard deviation = 14.27 Sample size = 31

Degrees of freedom = 31 - 1 = 3