Question

Assuming that the population is normally​ distributed, construct a 95​% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

Sample A: 1 4 4 4 5 5 5 8

Sample B: 1 2 3 4 5 6 7 8

a. Construct a 95​% confidence interval for the population mean for sample A.

b. Construct a 95​% confidence interval for the population mean for sample B.

c. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

Answer 1

Answer:-

From the above information

c.

Here we observed that range and mean of both samples are same but standard deviation of both the samples are different that is why these two samples produce different confidence interval because standard deviation measures spread of the data and here spread of both samples are different.Mean and sometimes range does not affect the spread of the data.