Question

If 95% and 98% confidence intervals were calculated from the same sample data in order to estimate the true cost of an appliance with a known population standard deviation, what differences would there be between them?

A) The standard errors would be different.
B) The point estimates of the population mean would be different.
C) The sample sizes would be different.
D) The z-statistics would be different.

Answer 1

D) The z-statistics would be different.

Explanation:

Confidence Interval can be calculated using M±ME where

• M is the sample mean
• ME is the margin of error from the mean

An margin of error (ME) from the mean can be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the corresponding z-statistic in the given confidence level

• s is the population standard deviation

• N is the sample size

If 95% and 98% confidence intervals were calculated from the same sample data, then M, s and N are same.

`(s)/(√(N) )` is called standard error. Since s and N are same the standard errors would also be same.

But, two tailed z-statistic for 95% confidence level is ≈1.96 where for 98% it is ≈2.33