Question 1083278: In an attempt to increase mathematics scores at a particular school, a twelve hour program has been created for students to work on key concepts and skills. In the ten years prior to the test, it was found that student scores were normally distributed with a mean score of 120 points and a standard deviation of 3.1 points.
Two groups of students at the same school are randomly selected and assigned to one of two groups. Students in Group A (forty students) are taught in four 3 hour sessions, while students in Group B (forty-five students) have six two hour sessions. Both groups finish their instruction the day before the exam. Group A’s results are an average score is 121 with a standard deviation of 7.25. Group B’s results are an average score is 124 with a standard deviation of 6. [12 marks]
a) Compare the two group’s results using a 95% confidence interval for each.
b) How do the results of each group compare to the past results? c) What recommendations do you have for the school in terms of the effectiveness of their initiative?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! somewhere along the line, i think you're missing sample size.
it does make a difference.
i used an online two sample t-test calculator and got significant results when the sample size was 40 or larger.
i couldn't find any references that said you could compare groups without knowing what the sample size of each group was.
i used graphpad online 2 sample t-test calculator.
it can be found here:
https://www.graphpad.com/quickcalcs/ttest1.cfm
i chose the test where you enter mean, standard deviation, and sample size.
since i didn't have sample size, i chose different sample sizes until the results became statistically significant between group A and B.
what i did was the following:
group A has a mean of 121 with a standard deviation of 7.25
group B has a mean of 124 with a standard deviation of 6.
the control group has a mean of 120 with a standard deviation of 3.1.
i did tests of group A compared to group B assuming group size was 10, 20, 30, 40
group B was the winner in all tests, but the tests didn't become statistically until the sample size was around 40 or more.
when the sample size was 40, i did the following:
i compared group A to B.
group B was the winner and the results were statistically significant.
i compared group A to the control group.
group A was the winner but the results were not statistically significant.
i compared group B to the control group.
group B was the winner and the results were statistically significant.
based on the sample size of 40, i concluded:
group B was better than both group A and the control group and the results were statistically significant.
group A was better tan the control group but the results were not statistically significant.
statistically significant means that the results were probably not due to chance variations in the sample mean.
a reasonable conclusion from this is that 6 two hour sessions produce better results than 4 three hours sessions and i would recommend they go to that based on the results of the test with sample size of 40 or more.
a picture of the results of the different test are shown below.
the first 2 lines tell you whether the test was statistically significant or not.
at 95% confidence level, if the two-tailed p-value was less then .05, then the test was considered to be statistically significant.
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