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Chapter 11: Q. 11 (page 735)

A large distributor of gasoline claims that 60%all cars 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's service stations in a large city. The results were as follows:

Carry out a significance test of the distributor's claim. Use a 5%significance level.

Short Answer

Expert verified

There is sufficient evidence to reject the distributor's claim.

Step by step solution

01

Given Information

Need to find whether there is sufficient evidence to reject the distributor's claim.

02

Explanation

Determine the observed frequencies and the chi-square subtotals:

The value of the test statistic is thus:

蠂2=1.8675+10.5125+0.8=13.15

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table C containing the t-value in the row

df=c-1=3-1=2

0.001<P<0.0025

If the P-value is less than or equal to the significance level, then the null hypothesis is rejected:

localid="1650541589569" P<0.05=5%鈬�RejectH0

There is sufficient evidence to reject the distributor's claim.

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