Question

For a population data set, σ = 14.30.

a. What should the sample size be for a 98% confidence interval for μ to have a margin of error of estimate equal to 5.10?

n =

b. What should the sample size be for a 95% confidence interval for μ to have a margin of error of estimate equal to 4.69?

n =

Answer 1

aSol)

S.D = 14.30

Margin of error ( E ) = 5.10

98% confidence interval

Alpha = 1 - 0.98 = 0.02

Alpha / 2 = 0.02 / 2 = 0.01

Z value for alpha / 2 = 0.01 is 2.33

n = (( Z * S.D ) / E ) ^ 2

= (( 2.33 * 14.30 )/ 5.10 ) ^ 2

= ( 6.53313 ) ^ 2

= 42.682

= 43

bsol)

S.D = 14.30

E = 4.69

95% confidence

Alpha = 1 - 0.95 = 0.05

Alpha / 2 = 0.05 / 2 = 0.025

Z value for alpha / 2 = 0.025 is 1.96

n = (( Z * S.D ) / E ) ^ 2

= (( 1.96 * 14.30 ) / 4.69 ) ^ 2

= ( 5.97611 ) ^ 2

= 35.714

= 36