The SAT scores of 20 randomly selected high school students has a mean of =1,185 and...

The SAT scores of 20 randomly selected high school students has a mean of =1,185 and a sample standard deviation s=168.0. Construct an 98% confidence interval for the true population mean and interpret this interval

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Expert Solution

Solution :

Given that,

= 1185

s = 168.0

n = 20

Degrees of freedom = df = n - 1 = 20- 1 = 19

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t_/2,df = t_0.01,19 =2.539

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.539 * (168.0 / $\sqrt$ 19) = 97.8577

The 98% confidence interval estimate of the population mean is,

- E < < + E

1185 - 97.8577 < < 1185+ 97.8577

1087.1423 < < 1282.8577

(1087.1423 , 1282.8577 )

orchestra answered 1 year ago

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