5.. **Title: Calculating the Margin of Error for a 95% Confidence Interval**---**Objective:**To find the margin of error for a 95% confidence interval for estimating the population mean, given the sample standard deviation and varying sample sizes. Additionally, to understand how sample size affects the margin of error.---**Problem Statement:**Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 90, with a sample size of:- **(i)** 400- **(ii)** 1600What is the effect of the sample size?---**Tasks:****(i)** Find the margin of error for a 95% confidence interval when the sample standard deviation equals 90 with a sample size of 400.- (Round to two decimal places as needed.)---

CI=0.95α=1-0.95=0.05s=90we have to find out the margin of error for the given dataformula of margin of error:=tc*sn1)n=400df=n-1=400-1=399tc:=tα/2,df=t0.05/2,399=1.966 [ from excel function , code :=TINV(0.05,399]ME:=tC*sn=2.966*90400=13.347=13.35 margin of error =13.352)n=1600df=n-1=1600-1=1599tc:=tα/2,df=t0.05/2,1599=1.961 [ from excel function , code :=TINV(0.05,1599]ME:=tC*sn=1.961*901600=4.41225=4.41 margin of error =4.41effect: if the sample size increased tha value of margin of error will be decreased