The General Social Survey described included random samples from two groups: US residents with a college degree and US residents without a college degree. For the 505 sampled US residents with a college degree, the average number of hours worked each week was 41.8 hours with a standard deviation of 15.1 hours. For those 667 without a degree, the mean was 39.4 hours with a standard deviation of 15.1 hours.

Required:

Conduct a hypothesis test to check for a difference in the average number of hours worked for the two groups.

Since is a bilateral test the p value would be:  

We have a very low p value so then we have enough evidence to conclude that the two population means are significantly different at a significance level of 1% for example.

Step-by-step explanation:

Data given

represent the mean for sample 1  college degree

represent the mean for sample 2  non college degree

represent the sample standard deviation for 1  

represent the sample standard deviation for 2  

sample size for the group 2  

sample size for the group 2  

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

(1)  

And the degrees of freedom are given by  

Statistic

With the info given we can replace in formula (1) like this:  

P value  

Since is a bilateral test the p value would be:  

We have a very low p value so then we have enough evidence to conclude that the two population means are significantly different at a significance level of 1% for example.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.