Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of steps per day they completed over the past week. The table below gives summary statistics for the daily step count of study participants based on the amount of coffee consumed. Consumption Mean Standard Deviation n <= 1 cup/week 7721 1848 17 2-6 cups/week 8212 1917 16 1 cup/day 9135 1491 28 2-3 cups/day 10678 1444 21 >3 cups/day 7428 593 30 Suppose you are interested in whether these data provide strong evidence that the average step count of study participants in the "1 cup/day" group and the ">3 cups/ day" group are different. What is the standard error of the point estimate for the difference?
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Step 1: The standard error of the difference between two means is calculated as: $$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$ where $s_1$ and $s_2$ are the sample standard deviations of the two groups, and $n_1$ and $n_2$ are the sample sizes of the two Show more…
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