The results of an annual Satisfaction Survey of policyholders who have had a claim with State Farm...

Question

The results of an annual Satisfaction Survey of policyholders who have had a claim with State Farm Insurance Company revealed a 80% satisfaction
 rate for claim service.

To check the accuracy of this claim, a random sample of State Farm claimants was asked to rate whether they were satisfied with the quality of the
 service.

(data worksheet: 1 = Satisfied and 2 = Unsatisfied)

Can we infer that the satisfaction rate is greater than 80%?

(Use a significance level of 0.05)

David · Accepted Answer

H0: p =.5 
H1: p>.5 
Since it a large sample we can use the central limit 
theorem to say that the distribution of proportions is 
approximately normal. We compute the test statistic: 
 
Notice that in this formula, we have used the 
hypothesized proportion rather than the sample 
proportion.

The results of an annual Satisfaction Survey of policyholders who have had a claim with State Farm Insurance Company revealed a 80% satisfaction rate for claim service. To check the accuracy of this...

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