Question

Do male and female servers at Swank Bar work the same number of hours? A sample of 65 female servers worked an average of 36 hours per week, with a standard deviation of 4. A sample of 65 male servers worked an average of 37 hours per week, with a standard deviation of 2. Let i and u2 represent the typical number of hours worked by all female and male servers at Swank Bar, respectively. Estimate with a 97% confidence level how many more hours female servers work. Round answers to the nearest hundredth.

___<μ1-μ2<___
Which of the following does your data suggest?
a. Female servers work more hours
b. Male servers work more hours
c. Female and male servers work about the same number of hours

Answer 1

The estimated difference in hours worked by female servers compared to male servers is between -2.177 and -0.823. This suggests that female servers work fewer hours compared to male servers at Swank Bar. Therefore correct option is a. Female servers work more hours

Step-by-step explanation:

To estimate how many more hours female servers work compared to male servers, we can use a confidence interval.

First, we calculate the margin of error using the formula:
Margin of Error = Z * (Standard Deviation / sqrt(sample size))

For the 97% confidence level, the Z-value is 1.96. The sample size is 65.

For female servers: Margin of Error = 1.96 * (4 / sqrt(65)) = 1.177

For male servers: Margin of Error = 1.96 * (2 / sqrt(65)) = 0.826

Next, we calculate the confidence interval for the difference in mean hours worked:
Confidence Interval = (mean of female servers - mean of male servers) ± Margin of Error

Confidence Interval = (36 - 37) ± 1.177 = -2.177 to -0.823

Therefore, the estimated difference in hours worked by female servers compared to male servers is between -2.177 and -0.823.

This suggests that female servers work fewer hours compared to male servers at Swank Bar.

Therefore correct option is a. Female servers work more hours