In a study of MP3 player popularity, 22% of people in a random sample of 1100 Americans age 12 and older indicated that they owned an MP3 player. The owners were 26% of the males and 18% of the females. Suppose that there were the same number of males and females in the sample of 1100. (Use a statistical computer package to calculate the P-value. Use p_males − p_females. Round your test statistic to two decimal places and your P-value to four decimal places.)
To calculate the P-value for this situation, we first need to determine the test statistic. In this case, the test statistic is the difference between the proportions of males and females who own an MP3 player, denoted as p_males - p_females.
Given that 26% of males and 18% of females own an MP3 player, we can calculate the test statistic as follows:
p_males = 0.26
p_females = 0.18
test statistic = p_males - p_females
= 0.26 - 0.18
= 0.08
Now, let's move on to calculate the P-value using a statistical computer package. Follow these steps:
1. Open the statistical computer package (e.g., R, Python, SPSS, etc.) on your computer.
2. Define the null hypothesis and alternate hypothesis for your test. In this case, the null hypothesis (H0) is that there is no difference between the proportions of males and females who own an MP3 player, while the alternative hypothesis (Ha) is that there is a difference.
H0: p_males - p_females = 0
Ha: p_males - p_females ≠ 0
3. Enter the data into the computer package. You need to provide the number of males and females in the sample, as well as the number of male and female MP3 player owners.
Number of males (n_males) = 550 (half of the sample size 1100)
Number of females (n_females) = 550 (half of the sample size 1100)
Number of male MP3 player owners (x_males) = n_males * p_males = 550 * 0.26
Number of female MP3 player owners (x_females) = n_females * p_females = 550 * 0.18
4. Use the computer package to conduct a Two-Proportion Z-test.
- Input the data and specify the test settings (e.g., two-tailed test, significance level).
- Run the test and obtain the test statistic and P-value.
The test statistic should be rounded to two decimal places, and the P-value should be rounded to four decimal places, as per the instructions given.
5. Interpret the results. If the P-value is less than the predetermined significance level (typically 0.05), we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
Please note that the specific steps for conducting a Two-Proportion Z-test may vary depending on the statistical software you are using. It's recommended to consult the documentation or user guide of your chosen computer package for more detailed instructions on running this specific test.