Question

Construct a 90% confidence interval to estimate the population mean using the data below.

x? = 90 |
? = 10 |
n = 30 |
N = 300 |

The? 90% confidence interval for the population mean is? (_,_).

Answer #1

Solution :

Given that,

= 90

= 10

n = 30

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_{/2}
= Z_{0.05} = 1.645

Margin of error = E = Z_{/2}* ( /n)

= 1.645 * (10 / 30)

= 3

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

- E < < + E

90 - 3 < < 90 + 3

87 < < 93

(87 , 93)

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