Although the link between obesity and one’s physical condition is well established, a research team stated that less was known about the relationship between obesity and one’s mental state of mind (Fontaine, Cheskin, & Barofsky, 1996). These researchers asked 312 obese people to complete a survey measuring social functioning. The researchers reported a sample mean (X) on social functioning of 77.10 and a population standard deviation (σ) of 22.30. Calculate a 95% confidence interval for the mean for the social functioning variable.

a. State the desired level of confidence.

b. Calculate the confidence interval and confidence limits.

(1) Calculate the population standard error of the mean (σ_X̅).

(2) Identify the critical value of z.

(3) Calculate the confidence interval and confidence limits.

c. Draw a conclusion about the confidence interval.