Question

7.3.42 probability that 25% or more of our sample will be bving in poverty Complete parts (a) and (b) below. a. Before doing any calculations, determine whether this probability is greater than 50% or less than 50%. Why? The answer Should be less than 50%, because 0.25 is greater than the population proportion of 021and because the sampling distreut n is app onately Normal mo answer ano ad be gea er man 50% because the resulting z-score will bo postive and the samping distribut on is approximately Normal. The answer should be less than 50%, because the resulting z soro wil be negative and the sampling distribution is approximately Normal. The answer should be greater than 50%, because 025 is greater than the population proportion of 021 and because the sampling distrbution is approximately Normal A o s C. D. ь. calculate te probablity that 25% or more of sample will be living in poverty. Assume the sample is collected in such a way that the conions using the CLT are met. P(p2025)-(Round to three decimal places as needed,)

Answer 1

$\mu_{\widehat p}$ = p = 0.21

$\dpi{100} \sigma_{\widehat p}$ = sqrt(p(1 - p)/n)

      = sqrt(0.21 * (1 - 0.21)/200)

      = 0.0288

P($\dpi{100} \widehat p$> 0.25)

= P(($\dpi{100} \widehat p$ - $\mu_{\widehat p}$ )/$\dpi{100} \sigma_{\widehat p}$> (0.25 - $\mu_{\widehat p}$ )/$\dpi{100} \sigma_{\widehat p}$)

= P(Z > (0.25 - 0.21)/0.0288)

= P(Z > 1.39)

= 1 - P(Z < 1.39)

= 1 - 0.918

= 0.082