Question

Use technology and the given confidence level and sample data to find the confidence interval for the population mean u.

Weight lost on a diet: 98% Confidence n=51 x=2.0 kg    s=4.2 kg

What is the confidence interval for the population mean u?

___ kg < u < ___ kg

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 2

sample standard deviation = s = 4.2

sample size = n = 51

Degrees of freedom = df = n - 1 = 51 - 1 = 50

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t _/2,df = t_0.01,50 = 2.403

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

= 2.403 * ( 4.2 / 51)

= 1.4

The 98% confidence interval estimate of the population mean is,

- E < < + E

2 - 1.4 < < 2 + 1.4

0.6 kg < < 3.4 kg