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The angle is less than 180 degrees, but more than 90 degrees.
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Answer:
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.