The results of a study of 268 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the7Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c belowTest score improvementsMean change in scoreStandard deviation of score changesMathVerbal176749tsho pomor we above nervalbraryb. Construct and interpret a 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutorfrect: 0ions(Round to three decimal places as needed.)Enter your answer in the edit fields and then click Check Answer>Check AnswerClear Allpartsremaining1256 AM10/30/2019aype here to search

Question
Asked Oct 30, 2019

Part b. Please show TI 84 steps

The results of a study of 268 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the
7
Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c below
Test score improvements
Mean change in score
Standard deviation of score changes
Math
Verbal
17
67
49
ts
ho po
mor we above nerval
brary
b. Construct and interpret a 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutor
frect: 0
ions
(Round to three decimal places as needed.)
Enter your answer in the edit fields and then click Check Answer
>
Check Answer
Clear All
parts
remaining
1256 AM
10/30/2019
a
ype here to search
help_outline

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The results of a study of 268 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the 7 Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c below Test score improvements Mean change in score Standard deviation of score changes Math Verbal 17 67 49 ts ho po mor we above nerval brary b. Construct and interpret a 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutor frect: 0 ions (Round to three decimal places as needed.) Enter your answer in the edit fields and then click Check Answer > Check Answer Clear All parts remaining 1256 AM 10/30/2019 a ype here to search

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Expert Answer

Step 1

Confidence interval when population standard deviation is not known:

The formula of confidence interval for the population mean when population standard deviation is not given is as follows.

Confidence interval = x f2 Tn
<u< X +t/2_Tn
where, Sample mean
S
=Margin of error
= Lower limit of the mean
= Upper limit of the mean
help_outline

Image Transcriptionclose

Confidence interval = x f2 Tn <u< X +t/2_Tn where, Sample mean S =Margin of error = Lower limit of the mean = Upper limit of the mean

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Step 2

Computing the 95% confidence interval for population mean:

Here, the sample mean (x-bar) is 9.

The sample standard deviation (s) is 49.

The confidence level is 0.95.

Thus, the level of significance, α is 0.05 (= 1 – 0.95).

The degrees of freedom (n − 1) is 267 (=268 − 1).

Step 3

T1-84 procedure to obtain 95% confidence interval:

  • Press the STAT button and highlight TESTS.
  • Scroll down to 8: TInterval
  • Highlight Stats and hit ENTER
  • Choose STATS, Enter values for S as 49, x-bar as 9, n as 268, a...

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Hypothesis Testing

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