Random samples of students were compared to see whether or not there was a difference in the proportion favoring the university's proposed switch from MWF (three-day) classes to MW and TR (two-day) classes. In the resident population 80 out of 200 favored the switch. In the commuter population, 120 out of 200 favored the switch. Conduct a hypothesis test at the .05 significance level to see if there is a difference in the proportion of residents and commuters who prefer the switch.

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of residents and commuters who prefer the switch.

Then, the null and alternative hypothesis are:

The significance level is 0.05.

The sample 1 (residents), of size n1=200 has a proportion of p1=0.4.

The sample 2 (conmuters), of size n2=200 has a proportion of p2=0.6.

The difference between proportions is (p1-p2)=-0.2.

The pooled proportion, needed to calculate the standard error, is:

The estimated standard error of the difference between means is computed using the formula:

Then, we can calculate the z-statistic as:

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

As the P-value (0.00008) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of residents and commuters who prefer the switch.

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