Question

A study was carried out to estimate the mean height in cm of 15 years old students in SMK Jeli. A random sample of 100 students was selected. Previous studies indicate that the population variance of the height of such students is 80cm. Suppose the sample mean height was 145cm. Find a 95% confidence interval for the mean height of all 15 years old students in the school

Answer 1

Confidence formula is written as:

$CI=(\bar{X}- Z\times\frac{\sigma}{\sqrt{n}})to(\bar{X}+ Z\times\frac{\sigma}{\sqrt{n}})$

Where;

Z value at 95% confidence interval = 1.96

σ (population deviation) = Square root of population variance = Square root of 80 = 8.94

n = 100

X-bar = 145

So, a 95% confidence interval for the mean height of all 15 years old students in the school is:

$CI=(145- 1.96\times\frac{8.94}{\sqrt{100}})to(145+ 1.96\times\frac{8.94}{\sqrt{100}})$

$CI=(145- 1.75)to(145+ 1.75)$

95% CI = (143.25, 146.75)