A statistics teacher wants to see whether there is a statistically significant d
ID: 3160063 • Letter: A
Question
A statistics teacher wants to see whether there is a statistically significant difference in the ages of day students and night students. A random sample of 31 students is selected from each group. The data are given below. Test the claim that there is difference in the mean ages of the two groups. Use = 0.01.
Day Students:
22 24 24 23 19 19 23 22 18 21 21
18 18 25 29 24 23 22 22 21 20 20
20 27 17 19 18 21 20 23 26
Evening Students:
18 20 25 23 20 24 25 23 23 23 19
25 20 21 24 19 23 27 23 24 23 24
20 21 20 24 21 21 20 28 27
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.01
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 21.58064516
X2 = 22.51612903
Calculating the standard deviations of each group,
s1 = 2.860934504
s2 = 2.541272224
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 31
n2 = sample size of group 2 = 31
Thus, df = n1 + n2 - 2 = 60
Also, sD = 0.687281009
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -1.361137378
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = +/- 2.660283029
Also, using p values, as this is two tailed,
p = 0.178560619
As |t| < 2.660, and P > 0.01, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant difference in the ages of day students and night students. [CONCLUSION]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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