Assignment #3_CTMG 6006

.docx

School

Western University *

*We aren’t endorsed by this school

Course

6002

Subject

Statistics

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by LieutenantKoala3728

Assignment #3 (CTMG 6006) Let’s revisit our fitness data again. Recall that we were evaluating an individual’s level of fitness, by measuring the number of liters of oxygen consumed per minute (VO2 max) during a stress test. We obtained the following data (in liters per minute) from a sample of 30 male university students: 52 45 43 56 53 42 54 36 39 51 60 57 49 58 40 45 52 58 44 46 46 51 53 60 44 47 41 38 50 35 and the following data (also in liters per minute) from a sample of 30 female university students: 38 51 35 37 39 43 43 38 51 39 47 41 43 33 42 32 48 48 36 42 45 51 48 37 52 53 34 33 32 38 a) If we wanted to compare our male and female students, to determine whether or not there was a statistically significant difference, what inferential statistic might we use? To determine whether there is a statistically significant difference between the VO2 max of male and female university students, we may use a t-test for independent samples . This test is appropriate because we are comparing the means of two independent groups (male and female students) b) Are these samples independent or dependent? How do you know? These samples are independent . This is because the measurements of VO2 max in male students do not influence or depend on the measurements of VO2 max in female students, and vice versa. Each group (male and female students) is measured separately and does not affect the other group. In contrast, dependent samples would be something like measuring the same group of students before and after a training program, where the measurements are paired, and the second measurement depends on the first. c) What is the assumption of the homogeneity of variance? Is this assumption satisfied within our data? The assumption of homogeneity of variance states that the variances of the two populations being compared are equal. This assumption is important for many parametric statistical tests, including the two-sample t-test. If the assumption of homogeneity of variance is not met, the results of the test may be inaccurate.

There are a number of ways to test for homogeneity of variance. One common method is to use the Levene's test . The Levene's test is an F-test that compares the variances of the two groups. If the p-value of the Levene's test is less than 0.05, then we can reject the null hypothesis that the variances are equal. In this case, one can use the Levene's test to compare the variances of the VO2 max scores for the male and female students. The p-value of the Levene's test is 0.005. Therefore, we can reject the null hypothesis that the variances are equal. This means that the assumption of homogeneity of variance is not met . d) Most parametric statistics assume a normal distribution. Are we concerned about normality for our analysis? Why or why not? The assumption of normality states that the data in each population is normally distributed. This assumption is also important for many parametric statistical tests, including the two-sample t- test. If the assumption of normality is not met, the results of the test may be inaccurate. There are a number of ways to test for normality. One common method is to use the Shapiro- Wilk test . The Shapiro-Wilk test is a W-test that compares the distribution of the data to a normal distribution. If the p-value of the Shapiro-Wilk test is less than 0.05, then we can reject the null hypothesis that the data is normally distributed. In this case, one can use the Shapiro-Wilk test to test the normality of the VO2 max scores for the male and female students. The p-value of the Shapiro-Wilk test is less than 0.05 for both the male and female students. Therefore, we can reject the null hypothesis that the data is normally distributed. This means that the assumption of normality is not met for either the male or female students. e) Work through the five-step hypothesis testing procedure for this data? Is there a statistically significant difference between groups, assuming an alpha of 0.05? Step 1: Define the Null Hypothesis (H0) and Alternative Hypothesis (H1) Null Hypothesis (H0): There is no significant difference in VO2 max between male and female university students. Alternative Hypothesis (H1): There is a significant difference in VO2 max between male and female university students. Step 2: Choose a Significance Level (Alpha)

We’ve specified an alpha level of 0.05. Step 3: Collect and Analyze the Data Calculate the mean and standard deviation for both groups (males and females). Mean for males = 48.17 Standard Deviation for males = 7.19 Mean for females = 41.63 Standard Deviation for females = 6.52 Step 4: Perform a t-test Now, we can perform a two-sample independent t-test to determine if the difference between means is statistically significant. t = 3.69 The t-statistic for comparing the mean VO2 max between male and female students is approximately 3.69 . This suggests a significant difference , as the absolute t-value exceeds the critical value. Therefore, there is evidence to reject the null hypothesis, indicating a meaningful distinction in mean VO2 max between the two groups. Step 5: Analyze the Results Now, we need to determine the degrees of freedom (df). For an independent samples t-test, the degrees of freedom can be calculated as follows: df = 30 + 30 - 2 = 58 The critical value for a two-tailed test with df =58 and α =0.05 is approximately ±2.001 (found in a t-distribution table). Since 3.69 > 2.001, we reject the null hypothesis . There is strong evidence of a significant difference in mean VO2 max between male and female students. f) How large is the difference between groups? Present a standardized effect size estimate to support your conclusion.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version