Question

a)
Determine the point estimate of the population mean and margin of error for the confidence interval Lower bound is 20, upper bound is 24. The point estimate of the population mean is . The margin of error for the confidence interval is










b)

Answer 1

Solution :

$\bar x$  = (Lower confidence interval + Upper confidence interval ) / 2

Sample mean = $\bar x$ = (20+24) /2 =22

point estimate=Sample mean = $\bar x$   =22

Margin of error = E = Upper confidence interval - $\bar x$   = 24-22=2

Margin of error = E =2

(B)

Solution :

Given that,

$\hat p$= 0.51

1 - $\hat p$ = 1 - 0.51 = 0.49

margin of error = E = 2% = 0.02

At 94% confidence level the z is ,

Z$\alpha$/2 = Z0.03 = 1.88 ( Using z table )

Sample size = n = (Z$\alpha$/2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (1.88 / 0.02)2 * 0.51 * 0.49

= 2208.1164

Sample size =2209