Question

Use technology and the given confidence level and sample data to find the confidence interval for the population mean mu μ. Assume that the population does not exhibit a normal distribution. Weight lost on a diet:

90% confidence n=41 x x=3.0 kg s=5.6 kg

What is the confidence interval for the population mean mu μ​? _<μ<_

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 3.0

sample standard deviation = s = 5.6

sample size = n = 41

Degrees of freedom = df = n - 1 = 40 - 1 = 40

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,40 = 1.684

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

= 1.684 * (5.6 / 41)

= 1.5

The 90% confidence interval estimate of the population mean is,

- E < < + E

3.0 - 1.5 < < 3.0 + 1.5

1.5 < < 4.5