Question

Use technology and the given confidence level and sample data to find the confidence interval for the population mean. Assume that the population does not exhibit a normal distribution.

Weight lost on a diet: 99% confindence n=41 dash above x = 4.0 kg s=5.9 kg

What is the confidence interval for the population mean μ ?

__kg < mean < __kg

Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed?

A. ​No, because the population resembles a normal distribution.

B. No, because the sample size is large enough.

C. Yes, because the sample size is not large enough.

D. Yes, because the population does not exhibit a normal distribution.

Answer 1

Solution :

Given that,

= 4.0kg

s = 5.9 kg

n = 41

Degrees of freedom = df = n - 1 = 41 - 1 = 40

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t /2  df} = t_0.005,40 = 2.704

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

= 2.704 * (5.9 / 41)

= 2.5

The 99% confidence interval estimate of the population mean is,

- E < < + E

4..0 - 2.5 < < 4.0 + 2.5

3.5 < < 6.5

Is the confidence interval affected by the fact that the data appear to be from a population that is not normally distributed

B. No, because the sample size is large enough.