Question

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.

Answer 1

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 = t_0.05,11 = 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)