Answer to Question #175773 in Statistics and Probability for Denisse Bisuña

Question

1.Who knows the game sipa? A Physical Education major sought to determine whether all Filipinos are familiar with this game. Among 1,500 respondents, 358 knew the game. Use 95% confidence to estimate the population proportion p and q. Interpret the sample data.

A. Find (^z_a/2)² given each of the following:

^-----------

E

a. With 90% confidence, E = 0.01.

b. With 90% confidence, E = 0.02.

c. With 95% confidence, E = 0.15.

d. With 95% confidence, E = 0.08

e. With 99% confidence, E = 0.05.

Answer 1

1.

$E=Z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$

$n=1500,p=358/1500=0.2387=23.87\%,\ q=76.13\%$

$E=1.96\sqrt{\frac{0.2387\cdot0.7613}{1500}}=0.0216=2.16\%$

The population proportion p and q are in 95% confidence interval with error 2.16%

A. a)

$(Z_{\alpha/2})^2=(1.65\pm0.01)^2$

$2.69\leq (Z_{\alpha/2})^2\leq 2.76$

b)

$(Z_{\alpha/2})^2=(1.65\pm0.02)^2$

$2.66\leq (Z_{\alpha/2})^2\leq 2.79$

c)

$(Z_{\alpha/2})^2=(1.96\pm0.15)^2$

$3.28\leq (Z_{\alpha/2})^2\leq 4.45$

d)

$(Z_{\alpha/2})^2=(1.96\pm0.08)^2$

$3.53\leq (Z_{\alpha/2})^2\leq 4.16$

e)

$(Z_{\alpha/2})^2=(2.58\pm0.05)^2$

$6.40\leq (Z_{\alpha/2})^2\leq 6.92$