A random sample of the ACT scores of 300 students at Big State University provided a...

A random sample of the ACT scores of 300 students at Big State University provided a sample mean score of 21.8 with a sample standard deviation of 5.632. Find the 95% confidence interval for the mean score of all Big State students who had taken the ACT.?
(a) (21.2, 22.4) (b) (21.0, 22.6) (c) (20.9, 22.7) (d) (20.3, 23.3) (e) (21.3, 22.3)

Solutions

Expert Solution

Solution :

Given that,

= 21.8

s = 5.632

n = 300

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * ( 5.632/ $\sqrt$ 300)

= 0.64

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

- E < < + E

21.8 - 0.64 < < 21.8 = 0.64

21.2< < 22.4

(21.2,22.4 )

correct answer is (a)

orchestra answered 1 year ago

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