Question

Companies often develop and test hypotheses about their products. For example, car manufacturers will test their cars to determine fuel efficiency and miles per gallon. To ensure that products are safe and that they perform as advertised, regulatory and consumer protection groups also test companies’ claims.

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 write 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? (Include your calculations).
List the null and alternative hypotheses for the one-tail test of the mean. Calculate the observed value of the test statistic and the associated p-value.
Is the observed test statistic in the critical region? Will the p-value be higher or lower than your alpha? (Include your calculations).
In your report, use the confidence interval information and the results of the hypothesis testing to provide support for your conclusions and recommendations to the company. Specifically:

What conclusions did you reach? What did you learn about the situation by using each method? Did one method offer more conclusive proof than another?
Based on your results, do you support the company’s claim that their minivans get 28 miles per gallon?
Summarize the details of your test methods and the results from each statistical method you used. Explain the findings so that executives from both the agency and the company can understand your conclusion.
Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future.

Answer 1

Hypothesis testing is a statistical process to validate claims about population parameters using sample data. The null and alternative hypotheses represent the status quo and the assertion being tested, respectively. Decisions are made based on the p-value in relation to a predetermined significance level, typically set at 0.05.

Step-by-step explanation:

Hypothesis testing in statistics is a method used to decide whether the data support a certain claim or hypothesis about a population parameter. This process involves the comparison of the null hypothesis, typically representing no effect or no difference, and the alternative hypothesis, which represents a significant effect or difference. It is a critical tool in making informed decisions in various fields such as business, engineering, medicine, and more.

Two-Tail Test Hypotheses

The null hypothesis (H0): The mean mpg is 28.
The alternative hypothesis (Ha): The mean mpg is not 28.

One-Tail Test Hypotheses

The null hypothesis (H0): The mean mpg is at least 28.
The alternative hypothesis (Ha): The mean mpg is less than 28.

The significance level (alpha) for the hypothesis test is typically 0.05, which is the threshold for determining whether the observed effect is statistically significant. If the p-value is less than the alpha level, the null hypothesis is rejected, indicating that the alternative hypothesis has enough evidence to be considered true.

In the given examples, calculations for mean, standard deviation, and the test statistic along with the determination of the p-value would be necessary to make a decision to support or reject the null hypothesis. Conclusions and recommendations would follow based on whether the data showed the cars met or did not meet the advertised mpg.