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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:

χ2=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%⇒RejectH0

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

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Most popular questions from this chapter

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Interpret the p-value from the calculator in context.

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) 99.

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(a) State appropriate hypotheses for testing whether these data give convincing evidence that the distribution of outcomes on this wheel is not what it should be.

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The expected count of cases of lymphoma in homes with an HCC is

(a) 79·31215.

(b) 10·21215.

(c) 79·3110.

(d) 136·31215.

(e) None of these.

Software gives test statistic χ2=69.8and P-value close to 0 . The correct interpretation of this result is

(a) the probability of getting a random sample of 4877teens that yields a value of χ2of 69.8or larger is basically 0.

(b) the probability of getting a random sample of 4877teens that yields a value of χ2of 69.8or larger if H0is true is basically 0.

(c) the probability of making a Type I error is basically 0.

(d) the probability of making a Type II error is basically 0.

(e) it's very unlikely that these data are true.
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