Statistics Proiect-Difference in Means We want to compare the mean GPA for femal
ID: 3263963 • Letter: S
Question
Statistics Proiect-Difference in Means We want to compare the mean GPA for females and males at Valencia. This project will ask you to take a random sample from the population of female GPAs and a random sample from the population of male GPAs. Use the Student Data I provided (same data as for the last project). The female GPAs are ID numbers 1 to 4573 and the male GPAs are ID numbers 4574 to 7903. Each person should generate their own random samples fromm these two groups. Show the random IDs and their corresponding GPAs. 1. what do the symbols 1 and 2 represent in the context of this problem? Be specific. 1 represents the mean GPA for all West Campus female students who have completed at least 30 credit hours. In order to calculate 1, the GPA scores for all 4,573 students will need to be summed and then divided by 4,573. 2 represents the mean GPA for all west Campus male students who have completed at least 30 hours. In order to calculate 2, the GPA scores for all 3,329 (7903-4574) students will need to be summed and then divided by 3,329. by 3,329, all 3,329ed at iea2 represets for al4s completed at 2. Take a random sample of twenty GPAs from each population (20 females and 20 males). Show the random IDs as well as the GPAs.Explanation / Answer
Solution:-
3)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Male = Female , G.P.A scores of male and female are same.
Alternative hypothesis: Male Female
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.1445
DF = 38
t = [ (x1 - x2) - d ] / SE
t = 0.554
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 38 degrees of freedom is more extreme than - 0.554; that is, less than -0.554 or greater than 0.554.
Thus, the P-value = 0.583
Interpret results. Since the P-value (0.583) is greater than the significance level (0.10), we have to accept the null hypothesis.
From the above, we have sufficient evidence in the favor of the claim that G.P.A scores of male and female are same.