A mathematics professor is interested in increasing the mathematical ability of
ID: 3397260 • Letter: A
Question
A mathematics professor is interested in increasing the mathematical ability of college students in remedial math classes. The professor obtains a random sample of ten students enrolled in remedial math this semester and begins the semester teaching these ten students using the new “Skills Building Program” (SBP) that the professor devised. The final exam these ten students are given is the same final exam the professor has used for the past 15 semesters, where the mean score is 12 and the standard deviation is 4 across these previous 15 semesters ( = 12 and = 4). High scores on this final indicate better mathematical performance. Test the professor’s hypothesis that the new SBP method improves scores on the final exam (and hence increases mathematical ability).
Final exam scores of students with new SBP method: 12, 10, 14, 13, 17, 12, 13, 17, 13, 15
With = .01, summarize the results of the hypothesis testing procedure by putting your results in journal form. Ignore the minus sign if your calculated z or t is negative.
A. r = .52, p < .01
B. z = .52, p > .01
C. z = 1.26, p > .01
D. z = 1.26, p < .01
E. t (9) = 2.28, p > .01
F. t (9) = 2.28, p > .01
G. t (10) = 3.36, p < .01
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 12
Ha: u > 12
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.01 ,
alpha = 0.01
zcrit = + 2.326347874
Getting the test statistic, as
X = sample mean = 13.6
uo = hypothesized mean = 12
n = sample size = 10
s = standard deviation = 4
Thus, z = (X - uo) * sqrt(n) / s = 1.264911064
Also, the p value is
p = 0.102951605
Thus,
OPTION C. z = 1.26, p > .01 [ANSWER, C]
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