A student at a four-year college claims that average enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 two-year colleges surveyed, the average enrollment was 5063 with a standard deviation of 4774. Of the 35 four-year colleges surveyed, the average enrollment was 5216 with a standard deviation of 8131. Conduct a hypothesis test at the 5% level.

The p value for this case would be given by:

Since the p value is higher than the significance level we don't have enough evidence to conclude that mean for 4 year college is higher than the mean for the 2 year college

Step-by-step explanation:

Data given

represent the mean for the two year college

represent the mean for the 4 year college

represent the sample standard deviation for the two year college

represent the sample standard deviation for the 4 year college

sample size for the group 1

sample size for the group 2  

Significance level provided

t would represent the statistic

System of hypothesis

We want to verify if average enrollment at four-year colleges is higher than at two-year colleges in the United States, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Since we don't know the population deviations the statisitc is given by:

(1)  

And the degrees of freedom are given by  

Replacing the info given we got:

P value  

The p value for this case would be given by:

Since the p value is higher than the significance level we don't have enough evidence to conclude that mean for 4 year college is higher than the mean for the 2 year college

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: