Question

Give the upper bound for a 95% confidence interval for a population mean generated from a sample of size n = 10 with a sample mean of x ¯ = 19.8oz and a standard deviation of s = 1.2oz.

Answer 1

Solution :

Given that,

= 19.8 oz.

s = 1.2 oz.

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

t,df = t0.05,9 = 1.833

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

= 1.833 * (1.2 / 10)

= 0.7

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

- E < < + E

19.8 - 0.7 < < 19.8 + 0.7

19.1 < < 20.5

(19.1,20.5)  

Upper Bound = 20.5 oz.