Question

In a pol of 1000 adults in July 2010, 540 of those polled said that schools should ban sugary snacks and soft driks Complute parts a and b belon H. p,0.50 Find the value of the test statissic z (Round to two decimal places as needed Find the value of the comesponding p-value for this test statisc aue Round to three decimal places as needed Do you reject or not reject ยาง nul hypothesis? Reject Ho Do not reject Ho O b Choose the best interpretation of the results you obtained in part A. The percentage ofall adults who favor banning is sigitcantly more than 50% B. The percentage of a.dts who favor barring is not spfcantly more than 50%

Answer 1

Solution :

Given that,

n = 1000

x = 540

$\hat p$ = x / n = 540 / 1000 = 0.54

P₀ = 0.50

1 - P₀ = 1 - 0.50 = 0.50

z = $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.54 - 0.50 / [$\sqrt$(0.50 * 0.50) / 1000]

= 2.53

z = 2.53

This is the two tailed test .

P(z > 2.53) = 1 - P(z < 2.53) = 1 - 0.9943 = 0.0057

P-value = 2 * P(z > 2.53) = 2 * 0.0057 = 0.0114

Here $\alpha$ is not given .