Question

Do male and female servers work the same number of hours? A sample of 25 female servers worked an average of 26 hours per week, with a standard deviation of 2. A sample of 11 male servers worked an average of 23 hours per week, with a standard deviation of 4. Let μ 1 and μ 2 represent the typical number of hours worked by all female and male servers, respectively. Construct a 90% confidence interval for μ 1 − μ 2 , assuming normal populations with unequal variances.

Answer 1

Answer:

Step-by-step explanation:

Given that

Group   Group One     Group Two  

Mean       26.00 23.00

SD                 2.00 4.00

SEM         0.40 1.21

N                     25     11    

where group I represents female servers and group II male servers.

We have to calculate confidence interval for 90% for difference in means

The mean of Group One minus Group Two equals 3.00

df = 34  

 standard error of difference = 0.993

t critical = 2.034 for 90% df 34

Hence confid. interval at 90%

=Mean diff ±2.034 * std error of diff

= (0.98, 5.02)