Final answer:
To evaluate the claim about nonhybrid versus hybrid sedan gas mileages, one must conduct a hypothesis test using the provided sample means, sample standard deviations, and known population standard deviations.
Step-by-step explanation:
To approximate the mean of the frequency distribution of gas mileages for cars, we need to compute a weighted average, where each gas mileage value is multiplied by its frequency and then divide the sum by the total number of cars. However, the question refers to conducting a hypothesis test to evaluate manufacturers' claim that nonhybrid sedan cars have a lower mean mpg than hybrid ones.
The steps for hypothesis testing are as follows:
- State the null hypothesis (μ1 = μ2) and the alternative hypothesis (μ1 < μ2), where μ1 is the mean mpg for nonhybrid sedans and μ2 is the mean mpg for hybrid sedans.
- Choose a significance level (α), commonly 0.05 for a 5 percent level.
- Calculate the test statistic using the given sample means, sample standard deviations, and population standard deviations.
- Determine the critical value from the standard normal distribution.
- Make a decision to reject or fail to reject the null hypothesis based on whether the test statistic falls in the rejection region defined by the critical value.