Hours spent studying per week were reported by students in a class survey. Stude
ID: 3158883 • Letter: H
Question
Hours spent studying per week were reported by students in a class survey. Students who say they usually sit in the front were compared to students who say they usually sit in the back. For the 99 students who reported that they usually sit in the front, the mean was 16.4 hours with a standard deviation of 10.85 hours. For the 94 students who reported that they usually sit in the back, the mean was 10.9 hours with a standard deviation of 8.41 hours. Assuming that the population standard deviations are different, find if there is a significant difference in number of hours studied between students who sit in the back and those who sit at the front. Explain what test you would perform, why etc. Identify the parameter of interest, write out the hypotheses in words and symbols.Explanation / Answer
As the sample sizes are both big (both greater than 30), then we can use z test as approximation to the t.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 16.4
X2 = 10.9
Calculating the standard deviations of each group,
s1 = 10.85
s2 = 8.41
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 99
n2 = sample size of group 2 = 94
Also, sD = 1.393392535
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = 3.947200707
where uD = hypothesized difference = 0
Also, the P value is, as this is two tailed,
p = 7.90703*10^-5
As Pvalue is very small , WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the number of hours studied between students who sit in front and in the back are different. [CONCLUSION]
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