Companies often develop and test hypotheses about their products. For example, car manufacturers test their cars to determine fuel efficiency and miles per gallon. To ensure that products are safe and perform as advertised, regulatory and consumer protection groups also test company 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 randomly select $35$ low$-$mileage fleet minivans to test their highway mileage. Your test results gave you the following data:

$29\mathrm{.}724\mathrm{.}527\mathrm{.}129\mathrm{.}829\mathrm{.}227\mathrm{.}027\mathrm{.}824\mathrm{.}129\mathrm{.}3$

$25\mathrm{.}926\mathrm{.}224\mathrm{.}532\mathrm{.}826\mathrm{.}827\mathrm{.}824\mathrm{.}023\mathrm{.}629\mathrm{.}2$

$26\mathrm{.}527\mathrm{.}727\mathrm{.}123\mathrm{.}724\mathrm{.}127\mathrm{.}225\mathrm{.}926\mathrm{.}727\mathrm{.}8$

$27\mathrm{.}327\mathrm{.}622\mathrm{.}825\mathrm{.}326\mathrm{.}626\mathrm{.}427\mathrm{.}126\mathrm{.}1$

Your report must align to the template and rubric, provided, and should include a brief introduction that provides a context for the assignment you have been given by your firm.

Part $1$: Sample Mean, Standard Deviation, and Confidence Interval

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Calculating the Confidence Interval

Replace this text with your response to the following in $75$ words $(1$ paragraph$)$: Calculate a $95\%$ confidence interval around your sample mean. Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Interpreting the Confidence Interval

Replace this text with your response to the following in $75$ words $(1$ paragraph$)$: Is the company$$s claimed mean inside your confidence interval?

Replace this text with your response to the following in $75$ words $(1$ paragraph$)$: What does that result indicate about the company$$s claim?

Part $2$: Hypothesis Testing: Two$-$Tail Test and One$-$Tail Test

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Calculating a Two$-$Tail Test

Replace this text with your response to the following in $75150$ words $(12$ paragraphs$)$: 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. Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Interpreting the Two$-$Tail Test

Replace this text with your response to the following in $75150$ words $(12$ paragraphs$)$: Is the observed test statistic in the critical region? Is the p$-$value higher or lower than your alpha?

Calculating a One$-$Tail Test

Replace this text with your response to the following in $75150$ words $(12$ paragraphs$)$: 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. Include your calculations. If your calculations are submitted separately, make note of where they can be found.

Interpreting the One$-$Tail Test

Replace this text with your response to the following in $75150$ words $(12$ paragraphs$)$: Is the observed test statistic in the critical region? Will the p$-$value be higher or lower than your alpha?

Part $3$: Conclusions

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Methods

Replace this text with your response to the following in $150225$ words $(23$ paragraphs$)$: 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?

The Manufacturer$$s Claim

Replace this text with your response to the following in $75$ words $(1$ paragraph$)$: Based on your results, do you support the company$$s claim that their minivans get $28$ miles per gallon?

Summary

Replace this text with your response to the following in $150225$ words $(23$ paragraphs$)$: 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.

Recommendations

Replace this text with your response to the following in $75$ words $(1$ paragraph$)$: Finally, present recommendations for actions that the company might take to use your findings to better serve their customers in the future.

Attachments

If applicable, list the filenames of any separate files you used to perform calculations. If you have no attachments, then indicate that in this section. Make sure that the file naming structure in this section matches the actual file names.

References

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Include appropriately formatted references to at least one scholarly source for each prompt to support the statements made in your report. Please refer to the Academic Writing Expectations Checklist for more information.