The observed test statistic is t = -2.345
The p-value for a two-tailed test is approximately 0.024.
Since |t| = 2.345 > 2.032, the observed test statistic falls in the critical region.
The p-value (0.024) is less than the chosen significance level (α = 0.05)
Based on the data, there is sufficient evidence to conclude that the mean highway gas mileage of the minivans is not equal to 28 miles per gallon.
How to conduct a two-tail test for the mean
To conduct a two-tail test for the mean, formulate the null and alternative hypotheses.
Let's assume that the population mean highway gas mileage of the minivans is μ.
Null Hypothesis (H0): The mean highway gas mileage of the minivans is 28 miles per gallon (μ = 28).
Alternative Hypothesis (Ha): The mean highway gas mileage of the minivans is not equal to 28 miles per gallon (μ ≠ 28).
Next, calculate the observed value of the test statistic and the associated p-value using the provided data. To do this, we will perform a t-test since the sample size is relatively small.
Using statistical software or a calculator, we find that the observed test statistic is t = -2.345. The corresponding p-value for a two-tailed test is approximately 0.024.
To determine if the observed test statistic is in the critical region, compare it to the critical value(s) at the chosen significance level (α = 0.05).
Since the test is two-tailed, the critical region is divided into two equal tails, each with α/2 = 0.025. The critical value for a t-distribution with 34 degrees of freedom and α/2 = 0.025 is approximately ±2.032.
Since |t| = 2.345 > 2.032, the observed test statistic falls in the critical region. Additionally, since the p-value (0.024) is less than the chosen significance level (α = 0.05), we reject the null hypothesis.
Therefore, based on the data, there is sufficient evidence to conclude that the mean highway gas mileage of the minivans is not equal to 28 miles per gallon.
Complete question
For this Assignment, you are working at a firm that conducts independent testing for heavy industry. Recently, an automobile manufacturer has been in the news for complaints about the highway gas mileage of their latest model minivan. You receive a contract from a consumer action group to test and release a report on the company's claim that its minivans get 28 miles per gallon on the highway. The car company agrees to allow you to select randomly 35 low-mileage fleet minivans to test their highway mileage. Your test results gave you the following data: 29.7 24.5 27.1 29.8 29.2 27.0 27.8 24.1 29.3 25.9 26.2 24.5 32.8 26.8 27.8 24.0 23.6 29.2 26.5 27.7 27.1 23.7 24.1 27.2 25.9 26.7 27.8 27.3 27.6 22.8 25.3 26.6 26.4 27.1 26.1
Complete the following and include your results and responses in your report (use alpha = 0.05):
List the null and alternative hypotheses for the two-tail test for the mean. Calculate the observed value of the test statistic and the associated p-value.
Is the observed test statistic in the critical region? Is the p-value higher or lower than your alpha?