Question

In 2009, 45.6% of motor vehicle accidents involved improper driving. In a recent survey of Weld County, it was found that out of 1250 accidents, 623 involved improper driving in some way. Is there sufficient evidence to conclude that the proportion of accidents involving improper driving has increased from the 45.6% at the α = 0.10 level of significance? Round computations to 3 decimal places.

find the test value and critical value

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.456

H_a : 0.456

Test statistic = z = 623 / 1250 = 0.4984

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.4984 - 0.456/ [(00456 * 0.544) / 1250]

= 3.01

P(z > 3.01) = 0.0013

= level of significance = 0.10

P-value <

Reject the null hypothesis .

Critical value = -1.282