Use the following table to answer the statistical analyses questions below. Two
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Question
Use the following table to answer the statistical analyses questions below. Two students are conducting research on the effect of sport supplements during an individual time trial. They collected times at a local amateur time trial during November and December 2007. a) What is the statistical null hypothesis being tested? b) What statistical analysis was performed below? c) What is the hypothesis most likely being tested? d) Based on the data above, b there a statistical difference between the two populations? e) Was the null hypothesis supported or rejected? f) Construct an appropriately labeled figure for the data in the table belowExplanation / Answer
Solution:-
x1 = 20.283, S.D1 = 0.12, n1 = 7
x2 = 19.383, S.D2 = 0.17, n2 = 7
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.
Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 0.07865
DF = 10.79
D.F = 11
t = [ (x1 - x2) - d ] / SE
t = 11.443
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.
Thus, the P-value = 0.00001
Interpret results. Since the P-value (0.00001) is less than the significance level (0.10), we cannot accept the null hypothesis.
From this we can conclude that there is sufficient evidence in the favor of the claim that there is significant difference between two populations.
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