A car company executive claims that a mean of 48.3 cars per dealership are being sold each month. An important stockholder thinks this claim is high and runs a test by sampling 30 dealerships. What conclusion can be reached of the sample mean is 45.4 cars with a standard deviation of 15.4 ?
There is sufficient evidence to prove the executive's claim is true.
There is sufficient evidence to prove the executive's claim is false.
The stockholder has sufficient evidence to reject the executive's claim.
The stockholder does not have sufficient evidence to reject the executive's claim.
There is not sufficient data to reach any conclusion.

Step 1 ：First, we need to calculate the test statistic. The test statistic is calculated using the formula \( \frac{{\text{{sample mean}} - \text{{population mean}}}}{{\text{{sample standard deviation}} / \sqrt{{\text{{sample size}}}}}} \). Given that the population mean is 48.3, the sample mean is 45.4, the sample standard deviation is 15.4, and the sample size is 30, we can substitute these values into the formula.

Step 2 ：The calculated test statistic is -1.0314255953019358.

Step 3 ：Next, we need to calculate the critical value for a one-sample t-test with 29 degrees of freedom (sample size - 1) at the 0.05 significance level. The critical value is -1.6991270265334977.

Step 4 ：We then compare the test statistic with the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 5 ：In this case, the test statistic (-1.03) is greater than the critical value (-1.70) at the 0.05 significance level. Therefore, we fail to reject the null hypothesis.

Step 6 ：This means that there is not enough evidence to support the stockholder's claim that the mean number of cars sold per dealership per month is less than 48.3.

Step 7 ：Final Answer: \(\boxed{\text{The stockholder does not have sufficient evidence to reject the executive's claim.}}\)