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Q. 11

Expert-verifiedFound in: Page 735

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

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.

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

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

Determine the observed frequencies and the chi-square subtotals:

The value of the test statistic is thus:

${\chi}^{2}=1.8675+10.5125+0.8\phantom{\rule{0ex}{0ex}}=13.15$

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

$df=c-1\phantom{\rule{0ex}{0ex}}=3-1\phantom{\rule{0ex}{0ex}}=2$

$0.001<P<0.0025$

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

localid="1650541589569" $P<0.05=5\%\phantom{\rule{0ex}{0ex}}\Rightarrow \text{Reject}{H}_{0}$

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

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