Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25

Answer 1

Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is 7.5

Answer:

The minimum sample size is
`n =97`

Explanation:

From the question we are told that

The margin of error is
`E = 1.25`

The standard deviation is
`s = 7.5`

Given that the confidence level is 90% then the level of significance is mathematically represented as

`\alpha = 100 - 90`

`\alpha =10\%`

`\alpha =0.10`

Next we obtain the critical value of
`(\alpha )/(2)` from the normal distribution table

The value is
`Z_{( \alpha )/(2) } = 1.645`

The minimum sample size is mathematically evaluated as

`n = \frac{Z_{(\alpha )/(2) * s^2 }}{E^2 }`

=>
`n = (1.645^2 * 7.5^2 )/(1.25^2 )`

=>
`n =97`