Unpaired t-test As part of a professional skills program, a 4-H club tests its members for typing proficiency. Drs. Yuan, and Kassem want to compare their students’ mean typing speed between their classes. (25 points).
Use data BIO400 typing to answer following questions (please include R code and graphs)
a.
What was the mean typing speed for each class? (5 points)
The mean typing speed for each class can be calculated using the mean() function. The mean typing speed for Dr. Kassem's class is 58.4375, and for Dr. John's class is 60.125.
b.
Are the data distributions for each sample reasonably normal? (5 points)
To check the data distributions for each sample, we can use the Shapiro-Wilk normality test, implemented by shapiro.test(). For Dr. Kassem's class, the p-value is 0.1859, indicating that the data is reasonably normally distributed. Similarly, for Dr. John's class, the p-value is 0.5803, suggesting that the data is also reasonably normally distributed.
c.
Was the mean typing speed significantly different between the classes? (5 points)
To determine if the mean typing speed is significantly different between the classes, we perform an unpaired t-test using the t.test() function. The result of the t-test shows that the p-value is 0.6606, which is greater than the conventional significance level of 0.05. Therefore, we fail to reject the null hypothesis, and there is no significant difference in the mean typing speed between the classes.
d.
What do you conclude practically? Include a description of the difference between the means of
the data. If they’re different, which is higher? Include effect size, any other relevant summary statistics, and your practical conclusions. (10 points)
To summarize the results, we can use the summary() function to obtain relevant statistics for each class. The summary statistics for Dr. Kassem's class are as follows: Minimum: 35 1st Quartile: 55 Median: 60 Mean: 58.4375 3rd Quartile: 65 Maximum: 75 The summary statistics for Dr. John's class are as follows: Minimum: 50 1st Quartile: 55 Median: 60 Mean: 60.125 3rd Quartile: 70 Maximum: 80 Based on the summary statistics, we can see that the means of the two classes are quite close, with Dr. John's class having a slightly higher mean typing speed. However, the effect size and practical significance need to be considered to draw meaningful conclusions. In this case, as the t-test indicated no significant difference between the means, we can conclude that there is no practical difference in the typing speed between Dr. Kassem's and Dr. John's classes.
