Q. 11 - The Practice of Statistics for AP

Question

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.

Step-by-Step Solution

Answer

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

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:

$$\begin{gathered} {\chi }^2=1.8675+10.5125+0.8 \\ =13.15 \end{gathered}$$

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

$$\begin{gathered} d f =c-1 \\ =3-1 \\ =2 \end{gathered}$$

$0.001<P<0.0025$

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

$$\begin{gathered} P<0.05=5\% \\ \Rightarrow \text{ Reject }{H}_0 \end{gathered}$$

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