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Expert-verified Found in: Page 735 ### The Practice of Statistics for AP

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.

See the step by step solution

## Step 1: Given Information

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

## Step 2: Explanation

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

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

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

There is sufficient evidence to reject the distributor's claim. ### Want to see more solutions like these? 