Use the 5-step hypothesis testing framework to answer the following 2 questions:

Step One: Stating the hypothesis
Step Two: Choosing the appropriate test statistic
Step Three: Developing a decision rule
Step Four: Calculating the value of the test statistic
Step Five: Stating the conclusion

Q1: A friend says at most only 50% of all people he has talked to have ever “unfriended” someone on Facebook (sample size 200). Your research finds 90% of Marketing Majors have (sample size 111). Are Marketing Majors more likely to be “unfriendly” than the average person?

Q2: On Facebook 3.8% of Male Marketing Majors have never unfriended someone while 15% of Female Marketing Majors have never unfriended someone. Does this mean Females are more friendly? (check SPSS datafile on blackboard for sample sizes)

Q1: A friend says at most only 50% of all people he has talked to have ever "unfriended" someone on Facebook (sample size 200). Your research finds 90% of Marketing Majors have (sample size 111). Are Marketing Majors more likely to be "unfriendly" than the average person?

Step One: Stating the hypothesis
- Null hypothesis (H0): The proportion of Marketing Majors who have "unfriended" someone on Facebook is equal to or less than 50%.
- Alternative hypothesis (Ha): The proportion of Marketing Majors who have "unfriended" someone on Facebook is greater than 50%.

Step Two: Choosing the appropriate test statistic
- Since we are comparing proportions, we can use the z-test for proportions.

Step Three: Developing a decision rule
- We need to determine a critical value or p-value for our test. We will use a significance level (α) of 0.05.
- If the p-value is less than 0.05, we will reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we will fail to reject the null hypothesis.

Step Four: Calculating the value of the test statistic
- Calculate the test statistic (z-score) using the sample proportion of Marketing Majors who have "unfriended" someone.
- z = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size)

Step Five: Stating the conclusion
- Compare the calculated test statistic with the critical value or p-value. If the calculated test statistic is greater than the critical value or the p-value is less than 0.05, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Q2: On Facebook 3.8% of Male Marketing Majors have never unfriended someone while 15% of Female Marketing Majors have never unfriended someone. Does this mean Females are more friendly? (check SPSS data file on blackboard for sample sizes)

Step One: Stating the hypothesis
- Null hypothesis (H0): The proportion of Female Marketing Majors who have never "unfriended" someone on Facebook is equal to or lower than the proportion of Male Marketing Majors who have never "unfriended" someone.
- Alternative hypothesis (Ha): The proportion of Female Marketing Majors who have never "unfriended" someone on Facebook is higher than the proportion of Male Marketing Majors who have never "unfriended" someone.

Step Two: Choosing the appropriate test statistic
- Again, since we are comparing proportions, we can use the z-test for proportions.

Step Three: Developing a decision rule
- We need to determine a critical value or p-value for our test. We will use a significance level (α) of 0.05.
- If the p-value is less than 0.05, we will reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we will fail to reject the null hypothesis.

Step Four: Calculating the value of the test statistic
- Calculate the test statistic (z-score) using the sample proportions of Male and Female Marketing Majors who have never "unfriended" someone.
- z = (proportion of Females - proportion of Males) / sqrt((proportion of Females * (1 - proportion of Females) / sample size of Females) + (proportion of Males * (1 - proportion of Males) / sample size of Males))

Step Five: Stating the conclusion
- Compare the calculated test statistic with the critical value or p-value. If the calculated test statistic is greater than the critical value or the p-value is less than 0.05, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Q1:

Step One: Stating the hypothesis
Null hypothesis (H0): The proportion of Marketing Majors who have "unfriended" someone on Facebook is equal to or less than 50%.
Alternative hypothesis (Ha): The proportion of Marketing Majors who have "unfriended" someone on Facebook is greater than 50%.

Step Two: Choosing the appropriate test statistic
Since we are comparing two proportions, we can use the z-test statistic.

Step Three: Developing a decision rule
Based on the alternative hypothesis (Ha) being "greater than," we will use a right-tailed test. We'll set the significance level (alpha) at 0.05.

Step Four: Calculating the value of the test statistic
To calculate the test statistic, we need to compare the sample proportion of Marketing Majors who have "unfriended" someone (90%) with the hypothesized proportion (50%).

Step Five: Stating the conclusion
If the calculated test statistic falls in the critical region, we will reject the null hypothesis and conclude that Marketing Majors are more likely to be "unfriendly" than the average person. Otherwise, if the test statistic does not fall in the critical region, we will fail to reject the null hypothesis.

Q2:

Step One: Stating the hypothesis
Null hypothesis (H0): The proportion of Female Marketing Majors who have never "unfriended" someone on Facebook is equal to or less than the proportion of Male Marketing Majors who have never "unfriended" someone.
Alternative hypothesis (Ha): The proportion of Female Marketing Majors who have never "unfriended" someone on Facebook is greater than the proportion of Male Marketing Majors who have never "unfriended" someone.

Step Two: Choosing the appropriate test statistic
Since we are comparing two proportions, we can use the z-test statistic.

Step Three: Developing a decision rule
Based on the alternative hypothesis (Ha) being "greater than," we will use a right-tailed test. We'll set the significance level (alpha) at 0.05.

Step Four: Calculating the value of the test statistic
To calculate the test statistic, we need to compare the sample proportions of Male and Female Marketing Majors who have never "unfriended" someone.

Step Five: Stating the conclusion
If the calculated test statistic falls in the critical region, we will reject the null hypothesis and conclude that Females are more friendly. Otherwise, if the test statistic does not fall in the critical region, we will fail to reject the null hypothesis.