In a study of 10000 car crashes it was found that 5720 of th

In a study of 10,000 car crashes, it was found that 5720 of them occurred within 5 miles of home. Use a .01 significance level to test that more than 70% of car crashes occur within 5 miles of home. State the null and alternative hypotheses, the pvalue, and conclusion.

Solution

Null hypothesis: The proportion of car crashes occcur within 5 miles at home is less than or equal to 70%

Alternative hypothesis: The proportion of car crashes occur within 5 miles at home is more than 70%

The test statistic z = (p=P)/SE(p)

where SE (p) = P*Q/n

Given P=0.7 Q=1-P=0.3; p= 5720/10000

Calculations :

P-value of the test is 1

We accept the null hypothesis. Hence there is no sufficient evidence to accept that more than 70% of car crashes occur within 5 miles of home.