In: Statistics and Probability
A random sample of size 15 is taken from a population assumed to be normal, with sample mean = 1.2 and sample variance = 0.6. Calculate a 95 percent confidence interval for population mean.
Point estimate = sample mean = = 1.2
sample standard deviation = s = 0.7746
sample size = n = 15
Degrees of freedom = df = n - 1 = 15 - 1 = 14
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df = t0.025,14 = 2.145
Margin of error = E = t/2,df * (s /n)
= 2.145 * (0.7746 / 15)
= 0.4
The 95% confidence interval estimate of the population mean is,
- E < < + E
1.2 - 0.4 < < 1.2 + 0.4
0.8 < < 1.6
A 95% confidence interval for population mean.(0.8 , 1.6)