1. A STAT 200 instructor wants to know if her students tend to score higher on t
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Question
1. A STAT 200 instructor wants to know if her students tend to score higher on the midterm exam than on the final exam. Data were collected from a representative sample of 46 students during the Fall 2017 semester. Data were paired by student. The mean difference, computed as midterm - final, was 1.3632 points with a standard deviation of 3.6362 points. [55 points]
A. In Minitab Express, conduct a paired means ttest to determine if there is evidence that midterm exam scores are higher than final exam scores in the population of all STAT 200 students. Use the five-step hypothesis testing procedure and remember to include all relevant Minitab Express output. You should not need to do any hand calculations.
Step 1:Check assumptions and write hypotheses
Step 2: Calculate the test statistic
Step 3:Identify the pvalue
Step 4:Make a decision
Step 5:State a “real world” conclusion
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: ud< 0
Alternative hypothesis: ud > 0
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).
s = sqrt [ (sum (di - d)2 / (n - 1) ]
s = 3.6362
SE = s / sqrt(n)
S.E = 0.53613
DF = n - 1 = 46 -1
D.F = 45
t = [ (x1 - x2) - D ] / SE
t = 2.543
where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.
Since we have a one-tailed test, the P-value is the probability that a t statistic having 45 degrees of freedom greater than 2.54.
Thus, the P-value = 0.007
Interpret results. Since the P-value (0.007) is less than the significance level (0.05), we have to reject the null hypothesis.
Reject H0. We have sufficient evidence in the favor of the claim that midterm exam scores are higher than final exam scores in the population of all STAT 200 students.
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