Final answer:
To evaluate the manufacturers' claim, a hypothesis test can be conducted. The null hypothesis states that the mean mpg of nonhybrid sedans is greater than or equal to the mean mpg of hybrid sedans, while the alternative hypothesis states that the mean mpg of nonhybrid sedans is less than the mean mpg of hybrid sedans. By calculating the test statistic and p-value using the provided data and significance level, we can determine whether there is enough evidence to support the manufacturers' claim.
Step-by-step explanation:
In statistics, we often conduct hypothesis tests to evaluate claims or statements about a population based on sample data. In this case, the manufacturers claim that nonhybrid sedan cars have a lower mean miles per gallon (mpg) than hybrid ones. To evaluate this claim, we can perform a hypothesis test.
Let's define our null and alternative hypotheses:
Null hypothesis (H0): The mean mpg of nonhybrid sedans is greater than or equal to the mean mpg of hybrid sedans.
Alternative hypothesis (H1): The mean mpg of nonhybrid sedans is less than the mean mpg of hybrid sedans.
Next, we can calculate the test statistic and the p-value using the provided data.
Using a one-sample t-test with the given sample means, sample standard deviations, and sample sizes, we can calculate the t-statistic and the corresponding p-value.
The test statistic is calculated as:
t = (sample_mean - hypothesized_mean) / (sample_standard_deviation / sqrt(sample_size))
In this case, the hypothesized mean is the mean mpg of hybrid sedans (31), the sample mean of nonhybrid sedans is 22, the sample standard deviation is 4, and the sample size is 31. Plugging in these values, we can calculate the t-statistic.
The p-value represents the probability of observing a t-statistic as extreme as the one calculated, assuming the null hypothesis is true. We can use the t-distribution table or statistical software to find the p-value.
If the p-value is less than the chosen significance level (usually 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that nonhybrid sedan cars have a lower mean mpg than hybrid ones. Otherwise, if the p-value is greater than the significance level, we fail to reject the null hypothesis and do not have enough evidence to support the claim.