Question

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

muμ. Assume that the population does not exhibit a normal distribution.

Weight loss on a diet: 95% confidence, n= 51, X bar= 3.0kg, s=5.3kg

What is the confidence interval for the population mean muμ​?

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

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

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

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

D. No, because the population resembles a normal distribution.

Answer 1

Here , n = 51 , = 3.0 and s = 5.3

We have to find a 95% confidence interval. We use the t distribution.

Degrees of freedom = n-1 = 50

At confidence level 95% and df = 50 , t = 2.01

The confidence interval is = t*s/n

= 3.0 1.49

=(1.51 , 4.49)

No, the confidence interval is not affected by the fact that the data appear to be from a population that is not normally​ distributed because:

C. because the sample size is large enough