Question

A JODA wanted to determine the average distance their members travel in a day. Since the driver-members are always busy, the JODA only managed to obtain 25 answers out of 1000 drivers. They find that the sample mean is 105, and the population standard deviation is 15. Determine the 95% and 99% confidence interval.

Answer 1

Solution

$\bar{X} = 105$

$\sigma =15$

n=25

$$C.I=\bar{X} \pm Z_{\alpha \over 2} {\sigma \over \sqrt{n} }$$

At 95% confidence interval :

$$C.I = 105 \pm 1.96 {({15 \over \sqrt{25}})}$$ $$=105 \pm 5.88$$ $$99.12 \le \bar{X} \le 110.88$$

At 99% confidence interval :

$$C. I= 105 \pm 2.58 ({15 \over \sqrt{25}})$$ $$=105 \pm 7.74$$

$$97.26 \le \bar{X} \le 112.74$$