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Chapter 11: T11.11 (page 765)

A large distributor of gasoline claims that 60%of all drivers stopping at their service stations choose regular unleaded gas and that premium and supreme are each selected 20%of the time. To investigate this claim, researchers collected data from a random sample of drivers who put gas in their vehicles at the distributor鈥檚 service stations in a large city. The results were as follows.

Carry out a test of the distributor鈥檚 claim at the 5%significance level.

Short Answer

Expert verified

There is sufficient evidence to support the claim that the distribution of type of gas purchased is not what the distributor claims, thus reject H0..

Step by step solution

01

Step 1. Given information

Given:

02

Step 2. Calculation

Hypotheses:

H0:pregular=0.6,ppremium=0.2,psupreme=0.2

Ha:At least one of the proportions is incorrect.

Conditions:

SRS: A random sample was used.

Independent: it seems reasonable that there would be more than 400people who stop at this gas station over a long period of time.

Count: the expected counts are 240,80,80, all of which are at least 5.

Chi square test for 渭1-渭2,

x2=13.15,P-value=0.0014,df=2

Thus, 伪=0.050.0014<0.05

Therefore, There is sufficient evidence to support the claim that the distribution of type of gas purchased is not what the distributor claims, thus rejectH0.

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