An SRS of 350 high school seniors gained an average of ?¯=20.58 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation ?=48.19. We want to estimate the mean change in score ?μ in the population of all high school seniors.(a) Using the 68 – 95 – 99.7 Rule or the ?-z-table (Table A), give a 68% confidence interval (?,?) for ? based on this sample.(Enter your answers rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)A: B:

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Asked Nov 4, 2019
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An SRS of 350 high school seniors gained an average of ?¯=20.58 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation ?=48.19. We want to estimate the mean change in score ?μ in the population of all high school seniors.

(a) Using the 68 – 95 – 99.7 Rule or the ?-z-table (Table A), give a 68% confidence interval (?,?) for ? based on this sample.

(Enter your answers rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

A:

 

B:

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Expert Answer

Step 1

It is given that,

Sample mean = 20.58

Standard deviation, sigma is 48.19.

The sample size, n is 350.

Step 2

The z-critical value for 68% confidence interval is approximately 1.

Th...

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CI xtz Vn 48.19 =20.58 t1 /350 - 20.58 ±2.576 (18.004, 23.156)

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