Show all of your work to compute the Z statistic for the items below.
Show all of your work to compute the Z statistic for the items below.
1. The average American college women works out 3.3 times a week. A random sample of 117 senior American college women average 3.8 times a week, with a standard deviation of 0.53 Are seniors statistically different from the population of American college women as a whole? Explain your answer in complete sentences after you find the Z score.
Z-score = 10.20
The Z score calculated is approximately 10.20. This value is significantly higher than the typical thresholds for Z scores (such as 1.96 for a 95% confidence level). This indicates that the average number of workout sessions per week for senior American college women (3.8) is statistically significantly different from the overall population mean (3.3). Senior college women work out more often than the general population of college women.
2. Research shows that 10% of the North Carolina population identifies as gay, 14% of a random sample of Robeson County residents (N= 527) identify as gay. Are Robeson County residents more likely than North Carolina residents to be gay? Explain your answer in full sentences.
The Z score calculated is approximately 3.06. Similar to Question 1, this Z score exceeds the common critical value thresholds, indicating a statistically significant difference. It suggests that Robeson County residents are more likely to identify as gay compared to the overall North Carolina population, where the proportion in Robeson County (14%) is statistically significantly higher than the state average (10%).