(5 points) A particular university has a main campus and a branch campus. They s
ID: 3359147 • Letter: #
Question
(5 points) A particular university has a main campus and a branch campus. They suspect that students are willing to travel farther to go to the main campus, while the branch campus students tend to be more local. They find that at the main campus, a sample of 25 students travels a mean of 114 miles, with a standard deviation of 38 miles. At the branch campus, a sample of 16 students had a mean of 102 miles, with a standard deviation of 30 miles. a. Write the null and alternative hypotheses. d.f Find the degrees of freedom. Find the test statistic. Do not assume the population variances are equal. 1 to dt-n-125-124 1.074 N-1 . 10-1-51.341 b. c. d. Find the p-value.Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Main = Branch
Alternative hypothesis: Main > Branch
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 = 10.68
b)
DF = 39
c)
t = [ (x1 - x2) - d ] / SE
t = 1.12
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 population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 1.12. We use the t Distribution Calculator to find P(t > 1.12).
d) Therefore, the P-value in this analysis is 0.135.
Interpret results. Since the P-value (0.135) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.