If a school district takes a random sample of 74 Math SAT scores and finds that...

If a school district takes a random sample of 74 Math SAT scores and finds that the average is 490, and knowing that the population standard deviation of Math SAT scores is intended to be 100. Find a 99% confidence interval for the mean math SAT score for this district.

≤μ≤

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 490

Population standard deviation = = 100
Sample size = n =74

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (100 / $\sqrt$ 74)

= 29.9

At 99% confidence interval mean is,

- E ≤μ≤ + E

490-29.9 ≤μ≤490+29.9

460.1≤μ≤ 519.9

(, )

orchestra answered 1 year ago

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