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.