Question

A statistics practitioner took a random sample of 80 observations from a population with a standard deviation of 25 and compute the sample mean to be 100.

(a) Estimate the population mean confidence interval with 90% confidence level, 95% confidence level and 99% confidence level.

(b) Describe the effect of increasing the confidence level on the confidence interval.

(c) At 99% confidence level, if the population standard deviation is reduced to 16, will the confidence interval be wider or narrower?

Answer 1

No. of observations,n = 80

Sample Standard deviation,s =25

Sample mean=100

a) We know that the confidence interval for mean at any confidence value is

where z^*= Z-value for confidence level

z* for 90% confidence value = 1.645 from the table

Hence

Similarly for 95% confidence level , z*=1.96

For 99% confidence level, z*=2.576

B) As we are noticing from above calculations, increasing the confidence level increases the confidence interval i.e. it increases error bound.

C) New population standard deviation =16

z* for 99% confidence level=2.576

Confidence interval will be=

As standard deviation is reduced, margin of error will be reduced results in narrow confidence interval than before.