Question

In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home (based on data from Progressive Insurance). Use a 0.01 significance level to test the claim that a majority of car crashes occur within 5 miles of home.

Answer 1

H0: p <= 0.5

Ha: p > 0.5

Sample proportion = 5720 / 11000 = 0.52

Test statistics

z = ( - p) / sqrt [ p ( 1 - p) / n ]

= ( 0.52 - 0.50 ) / sqrt [ 0.5 * 0.5 / 11000 ]

= 4.20

p-value = P(Z > z)

= P(Z > 4.20)

= 0 (From Z table)

Since p-value < 0.05 significance level, reject H0.

We have sufficient evidence to conclude that majority of car crashes occur within 5 miles of home.