In a sample of 120 randomly selected people in city a, 5% prefer eating salad after the main course. in a sample of 120 randomly selected people in city b, 8% prefer eating salad after the main course. check that the conditions are met for a hypothesis test to compare the population proportion of people that prefer eating salad after the main course in city a to the proportion in city b.

There is no enough evidence that the proportions are different.

Step-by-step explanation:

We have to perform a hypothesis test on the difference of proportions.

In this case, the sample size is equal.

The null and alternative hypothesis are

The significance level is assumed to be 0.05.

The weighted average p, as the sample sizes are the same, is the average of both proportions:

The standard deviation is

The z-value for this sample is:

The P-value for z=-0.9375 is P=0.3485.

The P-value (0.35) is greater than the significance level (0.05), so the null hypothesis is failed to reject.

There is no enough evidence that the proportions are different.