Question

In a sample of 169 trees, we found that a pear tree grow to average height of 32 feet and a sample standard deviation of 5 feet. The distribution is approximately normal. Find the 95% confidence interval for the mean population.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 32

sample standard deviation = s = 5

sample size = n = 169

Degrees of freedom = df = n - 1 = 168

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,168 = 1.914

Margin of error = E = t_/2,df * (s /n)

= 1.914 * (5 / 169)

= 0.736

The 95% confidence interval estimate of the population mean is,

- E < < + E

32 - 0.736 < < 32 + 0.736

31.264 < < 32.736

(31.264 , 32.736)