Chapter 11, Problem T11.11SPT

To determine

To calculate: test of the distributor’s claim at the $5\%$ significance level.

Answer to Problem T11.11SPT

There is sufficient evidence to support the claim that the distribution of type of gas purchased is not what the distributor claims, thus reject $H_0$ .

Explanation of Solution

Given information:

  

Calculation:

Hypotheses:

  $H_0:p_{regular}=0.6,p_{premium}=0.2,p_{\sup reme}=0.2$

  $H_a:$ 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 $400$ people 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 ${\mu }_1-{\mu }_2$ ,

  $x^2=13.15,P-value=0.0014,df=2$

Thus, $\alpha =0.05$

  $0.0014<0.05$

Therefore, There is sufficient evidence to support the claim that the distribution of type of gas purchased is not what the distributor claims, thus reject $H_0$ .