Question

According to the statistics reported, a surprsing number of car crashes are not covered by insurance. Simple results, consistent with the report, showed 41 of 183 vehicals were not covered by by insurance. Test the hypothesis that the porportion of vehicles not covered by insurance is 17% at .1 level of significance. Find the critical value, test statistic, and the P value Reject of fail to reject the null? then construct a 80% confidence interval for the true proprotion of vehicles not covered by insurance. type answers the the 4th decimal

Answer 1

H0 : p = 0.17
Ha: p not equals to 0.17

Critical value = +/- 2.576

test statistics:

P = 41/183= 0.2240
z = ( P -p )/sqrt(p*(1-p)/n)
= (0.2240 - 0.17)/sqrt(0.17 *(1-0.17)/183)
= 1.9447

p value = .0518

Fail to reject H0

z value at 80% =1.2816

CI = 0.2240 +/ - 1.2816 *(sqrt(0.2240 * (1-0.2240)/183))
= (0.1845,0.2635)