Question

Do male and female servers at Swank Bar work the same number of hours? A sample of 60 female servers worked an average of 29 hours per week, with a standard deviation of 3. A sample of 60 male servers worked an average of 22 hours per week, with a standard deviation of 2.

Let μ1 and μ2 represent the typical number of hours worked by all female and male servers at Swank Bar, respectively. Estimate with a 90% 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?

• Female servers work more hours
• Female and male servers work about the same number of hours
• Male servers work more hours

Answer 1

Answer:

Do male and female servers at Swank Bar work the same number of hours? A sample of 60 female servers worked an average of 29 hours per week, with a standard deviation of 3. A sample of 60 male servers worked an average of 22 hours per week, with a standard deviation of 2.

Let μ1 and μ2 represent the typical number of hours worked by all female and male servers at Swank Bar, respectively. Estimate with a 90% confidence level how many more hours female servers work. Round answers to the nearest hundredth.

6.23 < μ1 −μ2< 7.77

Which of the following does your data suggest?

The lower limit 90% CI for mean difference is above 0 value. Therefore,

• Female servers work more hours

CI = (21-12) Et * se

Population 1 Sample
Sample Size	60
Sample Mean	29
Sample Standard Deviation	3
Population 2 Sample
Sample Size	60
Sample Mean	22
Sample Standard Deviation	2
Intermediate Calculations
Population 1 Sample Degrees of Freedom	59
Population 2 Sample Degrees of Freedom	59
Total Degrees of Freedom	118
Pooled Variance	6.5000
Standard Error	0.4655
Difference in Sample Means	7.0000

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	90%
Intermediate Calculations
Degrees of Freedom	118
t Value	1.6579
Interval Half Width	0.7717
Confidence Interval
Interval Lower Limit	6.2283
Interval Upper Limit	7.7717