questiol Completion Status: Question 7 of 10> Moving to the next question preven
ID: 3321870 • Letter: Q
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questiol Completion Status: Question 7 of 10> Moving to the next question prevents changes to this answer. Question7 0 points Save Answer Leslie is interested in testing whether the performance of girls and boys on a standardized ma test differs. She collects data from 63 girls and 51 boys, who were randomly selected from a elementary school. The mean score for girls is 76 (s 13), and the mean score for boys is 71 s 8 What test should Leslie use, and what are the basic results of that analysis if sM1-M2 - 2.08 alpha is set at.011? local T TT Arial 3 (12pt)Explanation / Answer
Solution:-
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 0.01. 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 = 2.08
DF = 112
t = [ (x1 - x2) - d ] / SE
t = 2.40
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 112 degrees of freedom is more extreme than -2.40; that is, less than -2.40 or greater than 2.40.
Thus, the P-value = 0.018
Interpret results. Since the P-value (0.018) is greater than the significance level (0.01), we have to accept the null hypothesis.
From the above test we have sufficient evidecne that there is no difference between performance of girls and boys.
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