( , ) The results of a study of 251 students who paid a private tutor to help th
ID: 3306627 • Letter: #
Question
( , )
The results of a study of 251 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both ents are reproduced in the table. Complete parts a through c below. Test score improvements Mean change in score Standard deviation of score changes Math 19 62 Verbal 46 a. Construct and interpret a 95% confidence interval for the population mean change in the Mathematics score for students who pay a private tutor. (Round to three decimal places as needed.)Explanation / Answer
Solution:
a)95% CI for population mean change in Mathematics score:
Formula : = M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)
Given,
Sample mean = M = 19
Sample standard deviation = s = 62 , sample size = n = 251
= 0.05 hence , z = 1.96
sM = (622/251) = 3.91
= M ± Z(sM)
= 19 ± 1.96*3.91
= 19 ± 7.67
95% CI is ,[ 11.33, 26.67]
b) 95% CI for population mean change in Verbal score:
Formula : = M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)
Given,
Sample mean = M = 11
Sample standard deviation = s = 46 , sample size = n =251
= 0.05 hence , z = 1.96
sM = (462/251) = 2.9
= M ± Z(sM)
= 11 ± 1.96*2.9
= 11 ± 5.69
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