(Use Excel). The marketing department at Insure-Me, a large insurance company, w
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Question
(Use Excel). The marketing department at Insure-Me, a large insurance company, wants to advertise that customers can save, on average, more than $100 on their annual automotive insurance policies (relative to their closest competitor) by switching their policies to Insure-Me. However, to avoid potential litigation for false advertising, they select a sample of 50 random policyholders and compare their premiums to those of their closest competitor. A portion of the data is presented below. Use Table 2.
Specify the competing hypotheses to determine whether the mean difference between the competitor’s premium and Insure-Me’s premium is over $100.
Using the appropriate commands in Excel, find the value of the test statistic and the p-value. (Do not round intermediate calculations. Round "Test statistic" value to 2 decimal places and "p-value" to 4 decimal places.)
(Click to select)Do not rejectReject(reject or do not reject) H0. At the 5% significance level, we (Click to select)cancannot(can or cannot) conclude the mean difference between the competitor’s premium and the “Insure Me” premium is more than $100.
(Click to select)Do not rejectReject(reject or do not reject) H0. At the 10% significance level, we (Click to select)cancannot(can or cannot) conclude the mean difference between the competitor’s premium and the “Insure Me” premium is more than $100.
(Use Excel). The marketing department at Insure-Me, a large insurance company, wants to advertise that customers can save, on average, more than $100 on their annual automotive insurance policies (relative to their closest competitor) by switching their policies to Insure-Me. However, to avoid potential litigation for false advertising, they select a sample of 50 random policyholders and compare their premiums to those of their closest competitor. A portion of the data is presented below. Use Table 2.
Explanation / Answer
a) H0: D 100; HA: D > 100
b)
Test statistic: 1.68358
p value = 0.04772
c)
At 0.05 significance level we reject the null hypothesis.
At the 5% significance level, we can conclude the mean difference between the competitor’s premium and the “Insure Me” premium is more than $100.
d) At 0.10 significance level we reject the null hypothesis.
At the 10% significance level, we can conclude the mean difference between the competitor’s premium and the “Insure Me” premium is more than $100.
t-Test: Two-Sample Assuming Unequal Variances Competitor's Premium "Insure-Me" Premium Mean 985.56 788.5 Variance 84185.109 81995.969 Observations 50 50 Hypothesized Mean Difference 100 df 98 t Stat 1.68358 P(T<=t) one-tail 0.04772 t Critical one-tail 1.66055 P(T<=t) two-tail 0.09545 t Critical two-tail 1.98447Related Questions
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