Question

Determine the margin of error for an 80​% confidence interval to estimate the population mean with sigmaequals51 for the following sample sizes. ​a) n equals 35 ​b) n equals 41 ​c) n equals 60 Click the icon to view the cumulative probabilities for the standard normal distribution

. ​a) When nequals35​, the margin of error for an 80​% confidence interval is____. ​(Round to two decimal places as​ needed.)

​b) When nequals41​, the margin of error for an 80​% confidence interval is ____. ​(Round to two decimal places as​ needed.)

​c) When nequals60​, the margin of error for an 80​% confidence interval is ____. ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

For 80% confidence interval Z value is 1.28

Let us consider the margin of error

i.e., Margin of error is expressed as E

So

E = Z * /sqrt(n) ---------------->(1)

= 51

(a)

n = 35,

Substitute the values in eq(1) then

E =1.28*51 /sqrt(35)

E = 65.28/sqrt(35)

E = 11.03

(b)

n = 41

Substitute the values in eq(1) then

E =1.28*51/sqrt(41)

E = 65.28/sqrt(41)

E = 10.20

(c)

n = 60

Substitute the values in eq(1) then

E =1.28*51/sqrt(60)

E = 65.28/sqrt(60)

E = 8.43