Question

1o) A simple random sample of size n is drawn! from a population that is normally distributed The sample mean x is found to be 108, and the sample Standard deviation, s, is found to be lo. Construct a go.i. confidence interval for N, if the sample size, n, is 25.

Answer 1

Sample mean $\bar{x} = 108$

Sample standard deviation

Sample size n = 25

Significance level $\alpha$ = 1- 90/100 = 0.1

Since, population sd is unknown we will use

t-critical value at 90% confidence level which is:

to.1/2.25-1 = 1.711

/* we can find it using excel function: =T.INV(0.1/2,24) */

Confidence Interval for $\mu$ is:

$CI = \bar{x} \pm t_{\alpha/2,n-1}\frac{s}{\sqrt{n}}$

$= 108 \pm \frac{1.711\times10}{\sqrt{25}}$

$= 108 \pm3.422$

Therefore,

$90\% \: is \: Confidence\: Interval=104.578 <\mu<111.422$ ans.