136 2. Where students study may be as important as how much they study. students
ID: 3051321 • Letter: 1
Question
136 2. Where students study may be as important as how much they study. students who have one setting in which they regularly study may perform differently than students who have no regular study location. To test this, a random sample of 15 Introductory Psychology students is asked to study their psychology material for one hour every day in a special quiet room in the university library. A second sample of 15 students from the same class is also asked to study their material one hour every day but rotates among various settings (dorm room, cafeteria, and library). At the end of the semester, point totals for the psychology class are compared, with the 1 2 following summary statistics obtained: study in One Setting study in Various Settings X,80 s12=106, 09 s2-156.25 n2-15 a. State H and H. b. What is teri t at =.05? c. What is sx? d. What is obt? e. Reject Ho? f. Interpret the findings.Explanation / Answer
Solution:-
a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
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.
b) tcritical = 2.0484
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).
c)
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 4.182
DF = 28
d)
t = [ (x1 - x2) - d ] / SE
t = 2.63
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 28 degrees of freedom is more extreme than -2.63; that is, less than -2.63 or greater than 2.63.
Thus, the P-value = 0.014
e)
Interpret results. Since the P-value (0.014) is less than the significance level (0.05), we have to accept the null hypothesis.
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