A car rental company is conducting a study regarding the types of car preferred

Question

A car rental company is conducting a study regarding the types of car preferred by customers at the company's various locations. The table below summarizes the reservations over a seven-day period at three of the company's locations. The company is willing to consider the 250 reservations at Location 1 as a random sample from the set of all reservations at Location 1, the 277 reservations at Location 2 as a random sample from the set of all reservations at Location 2, and the 272 reservations at Location 3 as a random sample from the set of all reservations at Location 3. Do these data provide sufficient evidence to indicate a difference in the distributions of the car types between the populations of reservations at the three locations? Provide statistical evidence to support your conclusion.

Explanation / Answer

null hypothesis: there is similarity in the distributions of the car type between the population of reservations at the three locations.

alternate hypothesis: there is difference in the distributions of the car type between the population of reservations at the three locations.

running a chi square test on above:

for above 6 degree of freedom and 0.05 level critical value of X2 =12.592

as above test stat 8.1536 is less then critical value we can not reject null hypothesis that distribution of car type is similar in all 3 locations.

Observed O Compact Standard Full size Other Total location 1 76 75 40 59 250 location 2 90 78 47 62 277 location 3 96 64 61 51 272 Total 262 217 148 172 799 Expected E=rowtotal*column total/grand total Compact Standard Full size Other Total location 1 81.977 67.897 46.308 53.817 250 location 2 90.831 75.230 51.309 59.630 277 location 3 89.191 73.872 50.383 58.553 272 Total 262 217 148 172 799 chi square =(O-E)^2/E Compact Standard Full size Other Total location 1 0.436 0.7430 0.8592 0.4991 2.537 location 2 0.008 0.102 0.362 0.094 0.566 location 3 0.520 1.319 2.237 0.974 5.051 Total 0.963 2.164 3.458 1.568 8.1536

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