(a)Comparison of GPA for randomly chosen college juniors and seniors:
xbar= 3.05, s1 = .20, n1 = 15, xbar2= 3.25, s2 = .30, n2 = 15, á = .025, left-tailed test.
calculate
d.f. ____________
Standard error ____________
t-calculated ____________
p-value ____________
t-critical ____________
can some just give the answers i have an f and I'm going to fail if i don't get a good grade so plz help.
To calculate the degrees of freedom (d.f.) for a comparison of GPA for randomly chosen college juniors and seniors, we can use the formula:
d.f. = (n1 - 1) + (n2 - 1)
In this case, n1 = 15 (number of juniors) and n2 = 15 (number of seniors). Plugging the values into the formula, we get:
d.f. = (15 - 1) + (15 - 1) = 28
So the degrees of freedom is 28.
Next, to calculate the standard error, we can use the formula:
Standard error = √((s1^2 / n1) + (s2^2 / n2))
In this case, s1 = 0.20 (standard deviation of juniors' GPA), s2 = 0.30 (standard deviation of seniors' GPA), n1 = 15 (number of juniors), and n2 = 15 (number of seniors). Plugging the values into the formula, we get:
Standard error = √((0.20^2 / 15) + (0.30^2 / 15)) = √((0.04 / 15) + (0.09 / 15)) = √((0.002667) + (0.006)) = √(0.008667) = 0.093
So the standard error is 0.093.
To calculate the t-calculated value, we can use the formula:
t-calculated = (xbar1 - xbar2) / standard error
In this case, xbar1 = 3.05 (mean GPA of juniors), xbar2 = 3.25 (mean GPA of seniors), and standard error = 0.093. Plugging the values into the formula, we get:
t-calculated = (3.05 - 3.25) / 0.093 = -0.20 / 0.093 ≈ -2.15
So the t-calculated value is approximately -2.15.
To calculate the p-value, we can consult a t-distribution table or use statistical software. Since this is a left-tailed test with an alpha level of 0.025, we are looking for the probability of obtaining a t-value less than -2.15. The p-value represents this probability.
Using the t-distribution table or software, we find that the p-value is approximately 0.018.
Lastly, to find the t-critical value, we need to consult a t-distribution table (or use software) with the given alpha level and degrees of freedom. For a left-tailed test with an alpha level of 0.025 and 28 degrees of freedom, the t-critical value is approximately -2.048.
So the t-critical value is approximately -2.048.
This looks like an independent groups t-test.
Here are a few hints:
1. d.f. for an independent groups t-test is this: n1 + n2 - 2
2. Use the denominator of the appropriate t-test as the standard error of the difference between the two means.
3. Use the appropriate t-test to calculate the t-test statistic.
4. P-value is the actual level of the t-test statistic (found using a t-table).
5. T-critical can be found using a t-table with the appropriate degrees of freedom for a one-tailed test.
I hope this will get you started.