In: Statistics and Probability
A sample of 12 items yields Picture = 48.5 grams and s = 1.5 grams. Assuming a normal distribution, construct a 90 percent confidence interval for the population mean weight.
Solution :
Given that,
= 48.5
s = 1.5
n = 12
Degrees of freedom = df = n - 1 = 12 - 1 = 11
) At 90% confidence level the t is ,
= 1 - 90% = 1 - 0.90 = 0.1
/ 2 = 0.1 / 2 = 0.05
t /2,df = t0.05,11 = 1.662
Margin of error = E = t/2,df * (s /n)
= 1.796 * (1.5 / 12) = 0.778 (ROUNDED)
The 90% confidence interval of the population mean is,
- E < < + E
48.5 - 0.778 < < 48.5 + 0.778
47.722 < < 49.278
(47.722,49.278)