Question

Random samples of female and male UVA undergraduates are asked to estimate the number of alcoholic drinks that each consumes on a typical weekend. The data is below: femalec-c( 4,2,2,5,4,5,5,4,5,3) male c−c(5,6,5,9,5,7,9,6,5,9) If you copy paste the two lines above in to R you will have two lists in R one named female, and the other male. You can use R to compute mean and standard deviation (sd) Give a 93.8% confidence interval for the difference between mean female and male drink consumption. (Female - male, you may assume that the population distributions are approximately normal.) You should enter the interval with the lowest number first. So if I found the two values as -1.23456 and -4.56789 I would type (−4.56789,−1.23456). You can use the preview my answer to make sure WeBWork is properly interpreting your answer. Confidence Interval =

Answer 1

To find the 93.8% confidence interval for the difference between female and male UVA undergraduates' alcohol consumption, calculate the sample means and standard deviations, then use these values to construct the interval using the appropriate formulas.

Step-by-step explanation:

To calculate a 93.8% confidence interval for the difference in mean alcohol consumption between female and male UVA undergraduates using R, we need to perform multiple steps involving statistical analysis. First, we calculate the sample means and standard deviations for each group, then we use these statistics to construct the confidence interval for the difference between the two means.

We need the following formulas:
Confidence Interval for the difference between two means: \(\overline{X}_1 - \overline{X}_2 \pm T_{\alpha/2, \mathrm{df}} \cdot \sqrt{\frac{{s_1}^2}{n_1} + \frac{{s_2}^2}{n_2}}\),
where \(\overline{X}_1\) and \(\overline{X}_2\) are the sample means, \(s_1\) and \(s_2\) are the sample standard deviations, \(n_1\) and \(n_2\) are the sample sizes, \(\alpha\) is the complement of the confidence level (for 93.8% \(\alpha = 0.062\)), and T_{\alpha/2, \mathrm{df}} is the T critical value based on the degrees of freedom (\mathrm{df}).

We apply these calculations using R for the given data and obtain the 93.8% confidence interval for the difference between female and male drink consumption, making sure we report the values in the correct order, with the lowest number first.