Question

A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean isx⎯ ⎯ x¯ = 840 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student's t. (a) Construct an interval estimate of μ with 98% confidence. (Round your answers to 3 decimal places.) The 98% confidence interval is from to

Answer 1

`(832.156, \ 847.844)`

Explanation:

Given data :

Sample standard deviation, s = 15

Sample mean,
`\overline x = 840`

n = 23

a). 98% confidence interval

`$\overline x \pm t_((n-1, \alpha /2)). (s)/(√(n))$`

`$E= t_(( n-1, \alpha/2 )) (s)/(\sqrt n)}`

`$t_((n-1 , \alpha/2)) (s)/(\sqrt n)$`

`$t_((n-1, a\pha/2))=t_((22,0.01)) = 2.508$`

∴
`$E = 2.508 * (15)/(√(23))$`

`$E = 7.844$`

So, 98% CI is

`$(\overline x - E, \overline x + E)$`

`(840-7.844 , \ 840+7.844)`

`(832.156, \ 847.844)`