Question

8. Confidence intervals for estimating the difference in population means

Elissa Epel, a professor of health psychology at the University of California–San Francisco, studied women in high- and low-stress situations. She found that women with higher cortisol responses to stress ate significantly more sweet food and consumed more calories on the stress day compared with those with low cortisol responses, and compared with themselves on lower stress days. Increases in negative mood in response to the stressors were also significantly related to greater food consumption. These results suggest that psychophysiological responses to stress may influence subsequent eating behavior. Over time, these alterations could impact both weight and health.

You are interested in studying whether college juniors or college sophomores consume more calories. You ask a sample of n₁ = 35 college juniors and n₂ = 40 college sophomores to record their daily caloric intake for a week.

The average daily caloric intake for college juniors was M₁ = 2,423 calories, with a standard deviation of s₁ = 237. The average daily caloric intake for college sophomores was M₂ = 2,679 calories, with a standard deviation of s₂ = 256.

To develop a confidence interval for the population mean difference μ₁ – μ₂, you need to calculate the estimated standard error of the difference of sample means, s(M1 – M2)(M1 – M2). The estimated standard error is s(M1 – M2)(M1 – M2) =57.25   .

Use the Distributions tool to develop a 95% confidence interval for the difference in the mean daily caloric intake of college juniors and college sophomores.

0123Standard Normalt Distribution

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The 95% confidence interval is256   to   .

This means that you are   % confident that the unknown difference between the mean daily caloric intake of the population of college juniors and the population of college sophomores is located within this interval.

Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is   to   .

This means that you are   % confident that the unknown difference between the mean daily caloric intake of the population of college juniors and the population of college sophomores is located within this interval.

The new confidence interval is   than the original one, because the new level of confidence is   than the original one.

Answer 1