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assume that test scores are normally distributed. A random sample of 25 SAT scores has a...

assume that test scores are normally distributed. A random sample of 25 SAT scores has a mean 1120 with a standard deviation 190. If (a,b) is the 95% confidence interval for the mean of all SAT scores constructed based on this sample, then, to the nearest whole number, a= b=

Math   Statistics-And-Probability   
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Answer #1

Solution :

Degrees of freedom = df = n - 1 = 24

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,24 = 2.064

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

= 2.064 * (190 / 25)

= 78

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

- E < < + E

1120 - 78  < < 1120 + 78

1042 < < 1198

(1042 , 1198)

a = 1042

b = 1198

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