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.

y = x + 95

y = 42 + 95

y=137 mm hg

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.