Chapter 8, Problem 72E

To determine

To test: The claim that there is a difference between proportions of that there will be an increase in gamification and significant increase in gamification.

Answer to Problem 72E

Solution: There is a difference between proportions.

Explanation of Solution

Calculation: The null and alternative hypotheses are

$\begin{array}{l}{H}_0:p_1=p_2\\ H_a:p_1\ne p_2\end{array}$

People who think that there will be no increase in gamification can be calculated as follows:

$\begin{array}{c}=1021\times \frac{42}{100}\\ =429\end{array}$

People who think that there will be a significant increase in gamification can be calculated as follows:

$\begin{array}{c}=1021\times \frac{53}{100}\\ =541\end{array}$

To test the significance, Minitab software is used. The steps to be followed are provided below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat $>$ Basic statistics $>$ 2 proportion.

Step 3: Select summarized data.

Step 4: Click on “option” button and choose significance level and alternative hypothesis.

Step 5: Select “Use test and interval based on normal distribution.”

Step 6: Click on OK.

Hence, the obtained z- score is $-4.96$ and the P-value is 0.000.

Conclusion: Since the p-value is 0.000, which is less than 0.05, the null hypothesis is rejected at 5% level of significance. It can be concluded that there is a difference between proportions of the result that states whether or not there will be an increase in gamification in the future.