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:

Females (Population 1): 5, 3, 6, 5, 5, 5, 5, 6, 2, 5

Males (Population 2): 4, 5, 5, 7, 4, 6, 5, 7, 3, 5

Give a 93.1% confidence interval for the difference between mean female and male drink consumption. (Assume that the population variances are equal.)

Answer 1

To find a 93.1% confidence interval for the difference between mean female and male drink consumption, use the two-sample t-test formula.

Step-by-step explanation:

To find a 93.1% confidence interval for the difference between mean female and male drink consumption, we can use the two-sample t-test formula. The formula is:

CI = (x1 - x2) ± t(α/2, df) * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

CI is the confidence interval

x1 and x2 are the sample means

t(α/2, df) is the critical value for the t-distribution

s1 and s2 are the sample standard deviations

n1 and n2 are the sample sizes

In this case, x1 is the mean of females, x2 is the mean of males, s1 is the standard deviation of females, s2 is the standard deviation of males, and n1 and n2 are the sample sizes. Once we calculate all these values, we can plug them into the formula to find the confidence interval.