Question

In Market Research, it is important to achieve a high percentage of responses
for the surveys. To improve this percentage you can include an initial question of
motivation that increases the interest of the respondent to complete it. They have been sent
questionnaires with a motivational question about the improvement of leisure spaces in a city,
a sample of 250 households, obtaining 101 responses. Other identical questionnaires without
motivational question have been sent to another independent sample of 250 households,
obtaining 75 answers. Perform a hypothesis test to determine if the question of
motivation increases the percentage of responses. Use 95% confidence level

Answer 1

Here the claim (alternative hypothesis) is

So test is right tailed. Following is the null hypothesis:

Here we have

Pooled sample proportion is

Standard error of the test is:

So test statistics will be

The p-value is:

p-value = 0.0073

Excel function used for p-value: "=2*(1-NORMSDIST(2.44))"

Since p-value is less than 0.05 so we reject the null hypothesis. That is there is evidence to conclude that the question of motivation increases the percentage of responses.