Question

(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=75 and s =5. assuming normality, the 99% confidence interval for the population mean is:__________

Answer 1

The 99% confidence interval is
`71.67 < \mu < 78.33`

Explanation:

From the question we are told that

The sample size is
`n = 15`

The sample mean is
`\= x = 75`

The standard deviation is
`s = 5`

Given that confidence is 99% then the level of significance is mathematically represented as

`\alpha = 100 - 99`

`\alpha = 1\%`

`\alpha = 0.01`

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

The value is

`Z_{( \alpha )/(2) } = 2.58`

Generally the margin for error is mathematically represented as

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

=>
`E = 2.58 * ( 5)/( √(15) )`

=>
`E = 3.3307`

The 99% confidence interval is mathematically represented as

`\= x -E < \mu < \= x +E`

=>
`75 - 3.3307 < \mu <75 + 3.3307`

=>
`71.67 < \mu < 78.33`