Question

Given p = 0.4 and N = 35 for the high income group, Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.1 significance level. a) Identify the correct alternative hypothesis: ou < .50 ou = .50 op < .50 op= .50 op > .50 ou > .50 VLV| LAA Give all answers correct to 3 decimal places. b) The test statistic value is: * Preview c) Using the P-value method, the P-value is: *

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p < 0.50

$\hat p$ = 0.4

P0 = 0.50

1 - P0 = 1 - 0.50 = 0.50

Test statistic = z =

= $\hat p$ - P0 / [$\sqrt$P0 * (1 - P0 ) / n]

= 0.4 - 0.50/ [$\sqrt$(0.50 * 0.50) /35 ]

Test statistic = z = -1.183

P(z < -1.183)

P-value = 0.118