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In: Statistics and Probability

Scholastic Aptitude Test (SAT) mathematics scores of a random sample of 100 high school seniors in...

Scholastic Aptitude Test (SAT) mathematics scores of a random sample of 100 high school seniors in the state of Texas are collected, and the sample mean and standard deviation are found to be 520 and 80, respectively. Find a 95% confidence interval on the mean SAT mathematics score for seniors in the state of Texas.

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Expert Solution

= Solution :


Given that,

sample mean = = 520

Population standard deviation =    = 80

Sample size n =100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )


Margin of error = E = Z/2 * ( /n)

= 1.96* ( 80 /  100 )

= 15.68
At 95% confidence interval IS

- E < < + E

520 - 15.68 <   <520 + 15.68

(504.32 , 535.68)

orchestra answered 1 year ago
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