Question

In: Statistics and Probability

3. A researcher is trying to determine the average SAT score for 2018 SAT test-takers. (which...

3. A researcher is trying to determine the average SAT score for 2018 SAT test-takers. (which is known to follow normal distribution). He gathers a sample of 11 students and calculates x ̄ = 990 and s = 230. What is the 95% confidence interval for the mean IQ of Canadians, based off of this sample?

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 990

sample standard deviation = s = 230

sample size = n = 11

Degrees of freedom = df = n - 1 = 10

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,10 = 2.228

Margin of error = E = t/2,df * (s /n)

= 2.228 * (230 / 11)

= 154.506

The 95% confidence interval estimate of the population mean is,

- E < < + E

990 - 154.506 < < 990 + 154.506

835.494 < < 1144.506

The 95% confidence interval for the mean IQ of Canadians, based off of this sample is (835.494 , 1144.506)

orchestra answered 1 year ago
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