Math Problem Statement

Does where you live affect your insurance rate? The mean auto insurance rate for 27 drivers in a large city is $1,832 per car with a standard deviation of $352 while the mean rate for 25 drivers in a rural area is $1,609 with a standard deviation of $232. At α = 0.05, can we conclude that drivers in the large city pay higher insurance rates than those in the rural area, assuming the population variances are equal? T-Distribution Table a. Calculate the test statistic. t=

Round to three decimal places if necessary b. Determine the critical value(s) for the hypothesis test. + Round to three decimal places if necessary c. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Two-Sample t-Test

Formulas

Test Statistic: t = (X̄_city - X̄_rural) / √(s_p^2 * (1/n_city + 1/n_rural))
Pooled Variance: s_p^2 = [(n_city - 1) * s_city^2 + (n_rural - 1) * s_rural^2] / (n_city + n_rural - 2)

Theorems

Central Limit Theorem
t-Distribution

Suitable Grade Level

Undergraduate Level