From previous studies, it is concluded that 76% of car crashes occur within 2 miles of the motorists home.

Question

From previous studies, it is concluded that 76% of car crashes occur within 2 miles of the motorists home. A researcher claims it has increased and decides to survey 100 adults. Test the researcher's claim at the a=0.05 significance level.Express the null and alternative hypotheses in symbolic form for this claim. After surveying 100 adult Americans, the researcher finds that 18 car crashes occur within 2 miles of the motorists home. Compute the test statistic.What is the p-value? Verify np(1-p).

Answer 1

n=100, alpha = .05, 1 tail test, use z distribution

null hypothesis is 76%

xbar = 18

xbar = np = 100(.18)

var = npq = 18(.82) =

s = sqrvar = sqr14.76 = about 3.84

Ho: mu = .76

H1: mu > .76 (claim is it increased)

z= (x-xbar)/s/sqrn

= (18-76)/3.84/sqr100

= -58/3.84/10

= -580/3.84

= about -151

z critical = about 1.65

z calc< z crit fail to reject Ho

-151 < 1.65

76% have crashes within 2 miles of home

if anything initial guess would be less than 76%

should have tested H1: mu<.76, not H1: mu>.76