Question

Which of the following is NOT a requirement for constructing a confidence interval for estimating a population mean with sigmaσ ​known?Choose the correct answer below.

A.The sample is a simple random sample.

B.Either the population is normally distributed or greater than>​30, or both.

C.The confidence level is​ 95%.

D.The sample measures a quantitative value.

Answer 1

Concepts and reason

A $1 - \alpha$ confidence interval for the population parameter is an interval cantered about the sample statistic with width equal to twice the margin of error. If many samples are taken from a population with the same sample size then the proportion of the constructed confidence intervals that will contain the population parameter is $1 - \alpha .$

The probability of success in a single trial of a binomial experiment is $p.$ this probability is a population proportion.

A point estimate is a single value estimate for a population parameter. The most biased point estimate of the population mean $\left( \mu \right)$ is equal to sample mean $\left( {\bar x} \right)$ and the population standard deviation is $\left( \sigma \right)$ equal to sample standard deviation $\left( s \right).$

Fundamentals

The confidence interval formula is,

$C.I = \bar x \pm {Z_{critical}}\left( {\frac{\sigma }{{\sqrt n }}} \right){\rm{ }}\left( \begin{array}{l}\\{\rm{When population }}\\\\{\rm{standard deviation known}}\\\end{array} \right)$

The most biased point estimate of the population mean $\left( \mu \right)$ is equal to sample mean $\left( {\bar x} \right)$ and the population standard deviation is $\left( \sigma \right)$ equal to sample standard deviation $\left( s \right).$

The most biased point estimate of the population mean $\left( \mu \right)$ is equal to sample mean $\left( {\bar x} \right)$ and the population standard deviation is $\left( \sigma \right)$ equal to sample standard deviation $\left( s \right).$

The population standard deviation is know, so we use standard normal test otherwise we use student $t -$ test.

The correct option is: C

The confidence level is 95%.

The confidence level is not a requirement for constructing a confidence interval for estimating a population mean with sigma known.

Ans:

The confidence level is 95%.