Elizabeth is a financial adviser for a car dealership with locations throughout the country. She wondered if sales of convertibles are relatively higher in warm weather cities than in cold weather cities. To test her theory, she collected random samples of cars sold throughout a one-year period for locations in San Diego and Boston. Out of 400 cars sold in San Diego, 52 were convertibles, and 34 out of 400 cars sold in Boston were convertibles. Is there evidence that the proportion of convertibles sold in San Diego is greater than the proportion in Boston? Assume that the conditions for the hypothesis test are satisfied. Let San Diego cars correspond to population 1 and Boston cars correspond to population 2. Identify the test statistic, rounding to two decimal places, and the p-value, rounding to three decimal places.
What is:
z= p-value=
Ans:
sample proportion 1=52/400=0.13
sample proportion 2=34/400=0.085
pooled proportion=(52+34)/(400+400)=0.1075
Test statistic:
z=(0.13-0.085)/sqrt(0.1075*(1-0.1075)*((1/400)+(1/400)))
z=2.05
p-value=P(z>2.05)=0.020
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