Perform a complete hypothesis test using a confidence of 95% (unless otherwise s

Question

Perform a complete hypothesis test using a confidence of 95% (unless otherwise stated in the problem itself) The complete hypothesis test includes hypotheses, test identification, comparisons of p-values to alpha (or the critical value approach), calculations, and a statement that describes your solution. Problem 3: An automobile insurance company selected samples of single and married male policy holders and recorded the number who made an insurance claim over the preceding three year period. Of 400 single male policy holders, 76 had made claims while of 900 married male policyholders, 90 had made claims. Do we have sufficient evidence to conclude that married male policy holders make fewer claims?

Explanation / Answer

Hypotheses:

H0: p1-p2=0 (there is no difference in proportion of claims made by single and married male policy holders)

H1:p1-p2>0 (proportion of claims made by riedmar male policy holders is lesser than single male policy holders)

Assumptions: Model: Independent random samples, level of measurement is nominal, sampling distribution is normal.

Because sample size are large, Z distribution will be used to find the test statistic. Alpah=0.05.

Test statistic:

Compute pooled sample proportion, phatp=(x1+x2)/(n1+n2)=(76+90)/(400+900)=0.1277

Z=(p1hat-p2hat)[sqrt{phatp(1-phatp)}sqrt{1/n1+1/n2}]=(76/400-90/900)/[sqrt{0.1277(1-0.1277)}sqrt{1/400+1/900}]

=4.49

p value:0.0000

Rejection rule: Per rejection rule based on value reject H0, if p value is less than alpha=0.05. Here, p value is less than 0.05, therefore, reject H0 and conclude that married male policy holders make fewer claims.

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