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Consumer Reports measures owner satisfaction of various automobiles by asking thesurvey question, "Considering factors such as price, performance, reliability, comfortand enjoyment, would you purchase this automobile if you had it to do all over again?(Consumer Reports website, January 2009 ). Sample data for 300 owners of four popularmidsize sedans are as follows.a. Conduct a test of independence to determine if the owner's intent to purchase againis independent of the automobile. Use a. 05 level of significance. What is your conclusion?b. Consumer Reports provides an owner satisfaction score for each automobile byreporting the percentage of owners who would purchase the same automobile if they could do it all over again. What are the Consumer Reports owner satisfaction scores for the Chevrolet Impala, Ford Taurus, Honda Accord, and Toyota Camry? Rank the four automobiles in terms of owner satisfaction.c. Twenty-three different automobiles were reviewed in the Consumer Reports midsizesedan class. The overall owner satisfaction score for all automobiles in this class was69. How do the United States manufactured automobiles (Impala and Taurus) compare to the Japanese manufactured automobiles (Accordand Camry) in terms of owner satisfaction? What is the implication of these findings on the future market share for these automobiles?

a. There is sufficient evidence to support the claim that the variables arenot independent.b. $56.98 \%, 61.97 \%, 76.92 \%, 70.77 \%$c. US manufactured automobiles have a lower owner satisfaction thenJapanese manufactured automobiles.

Intro Stats / AP Statistics

Chapter 11

Comparisons Involving Proportions and a Test of Independence

Descriptive Statistics

Confidence Intervals

The Chi-Square Distribution

Temple University

Cairn University

Oregon State University

Lectures

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04:00

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So in this problem, we want to see whether the market shares among drop top three passenger cars have changed during the 1st 3/4 of 2004. So are no hypothesis would be that these cars haven't changed. So the proportion of market shares for Camry would still be 0.37 proportion of market share for ah cord our Honda will still be for the accord would still be 0.34 and the proportion of cars sold that are tourists would still be 0.29 And our alternative hypothesis would be that the population proportions are not the same are not all the same as before. So this would be our no on alternative hypotheses. And in order to test these, we will need to come up with a chi squared goodness of fit and the chi square Goodness of fit is equal to the sum from I equals one to the number of treatment groups of the difference between our observed frequency Finest are expected frequency squared over the expected frequency. So this is for each treatment group. So first we have to come up with, uh, the observed frequency. So let me write that right, That's down here. So for our camera e, we had an observed frequency of 4 80 for our accord. We had observed frequency of 3 90 end for our tourists. We had observed frequency of 3 30 Let me just move this further down of 3 30 And now we need to come up with an expected frequency for each of these and the expected frequency simply the our total times, the proportion and we can get a total by adding all these values are looking at the question. So our total is equal to 1200. Um, and our proportion is given as the following. So over here will be our proportion. And here will be our expected value. And this would be our ah, car type. So here we have Camry accord and tourists. So the expected proportion for camera would be 0.37 This the expected proportion for accord would be point before expected proportion for tourist would be 0.0.29 and 0.37 times 1200 is equal to 4 44 and the ex and 0.34 times 1200 is equal to 408 and 0.29 times 1200 is equal to 3 48 So our chi squared is going to be equal to the sum of the difference between the following value squared over these expected values. So it would be 4 80 minus 4 44 squared over 4 44 plus 3 90 minus 408 squared over for a wait plus 3 30 minus 3 48 squared over 3 48 And with this we get a chi squared value of approximately 4.64 So now we have this chi squared value, but we need to come up with a P value in order to come up with R P value. We also need a degrees of freedom. So this right here chi squared equals 4.64 and our P value is going to be equal to art. Our P value is dependent on our chi squared in our degrees of freedom. Degrees of freedom is a number of treatments groups, treatment groups we have minus one is equal to three minus one, which is equal to so our kaist r r p value. Given that hark I squared is 4.64 4.64 and two degrees of freedom is going to be equal to, um, it would be between 0.5 and 0.1 is between 0.5 and 0.1, and we're testing this against an Alfa 0.5 So because our Alfa of 0.5 is less than I were, Ah, point our P value, which is less than 0.1, we have insufficient and evidence to reject the NOL insufficient evidence to reject the no. So what does that mean? We can't conclude that there is a difference in the market share among top three passenger cars in the first quarter of 2004.

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