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In: Statistics and Probability

A large gasoline distributor claims that 65% of all vehicle owners who use its service stations...

A large gasoline distributor claims that 65% of all vehicle owners who use its service stations choose regular unleaded gas, 20% choose mid-grade unleaded gas, and 15% choose premium unleaded gas. To investigate this claim, researchers collected data from a random sample of drivers who filled up their vehicles at the distributor's service stations in a large city. The results were 305 regular, 121 mid-grade, and 74 premium gas purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.

Solutions

Expert Solution

null hypothesis:Ho: Sample proportion of different fuel is same as claimed by distributor

Alternate hypothesis:Ha: Sample proportion of different fuel is different from as claimed by distributor

degree of freedom =categories-1= 2
for 2 df and 0.05 level of signifcance critical region       χ2= 5.991

Applying chi square goodness of fit test:

           relative observed Expected residual Chi square
category frequency Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
Unleaded 0.65 305 325.00 -1.11 1.231
Mid-grade 0.20 121 100.00 2.10 4.410
Premium 0.15 74 75.00 -0.12 0.013
total 1.000 500 500 5.654

as test statistic 5.654 does not fall in rejection region; we can not reject null hypothesis

we do not have evidence to conclude that Sample proportion of different fuel is different from as claimed by distributor

orchestra answered 2 years ago
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