10. The grades of students are normal distributed. In a class of 10 students the average...

10. The grades of students are normal distributed. In a class of 10 students the average grade on a quiz is 16.35, with a standard deviation of 4.15. ( 3 marks ) a) Find the 90% confidence interval for the population mean grade. b) If you wanted a wider confidence interval, would you increase or decrease the confidence level?

Solutions

Expert Solution

Given that,

= 16.35

s =4.15

n = 10

Degrees of freedom = df = n - 1 = 10- 1 = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,9 = 1.833 ( using student t table)

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

= 1.833 * ( 4.15/ $\sqrt$ 10) = 2.4055

The 90% confidence interval estimate of the population mean is,

- E < < + E

16.35 - 2.4055< <16.35 + 2.4055

13.9445 < < 18.7555

( 13.9445 , 18.7555)

(B) increase

orchestra answered 11 months ago

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