Question

Assuming that the population is normally​ distributed, construct a 99​% 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

Construct a 99​% confidence interval for the population mean for sample A.

less than or equalsmuless than or equals Type integers or decimals rounded to two decimal places as​ needed.)

Construct a 99​% confidence interval for the population mean for sample B.

less than or equalsmuless than or equals ​(Type integers or decimals rounded to two decimal places as​ needed.)

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

A. The samples produce different confidence intervals because their critical values are different.

B. The samples produce different confidence intervals because their sample sizes are different.

C. The samples produce different confidence intervals because their standard deviations are different.

D. The samples produce different confidence intervals because their medians are different.

Answer 1

So., 99?% confidence interval for the population mean for sample A is 2.744868 to 6.255132 &

99?% confidence interval for the population mean for sample B is 2.269267 to 6.730733

& As shown above the sd i.e. std devaition of A &B are quite difrent and so we can say that

C. The samples produce different confidence intervals because their standard deviations are different.

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