BS2002_

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2002

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Jan 9, 2024

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Assessment Template: Minivan MPG Report Introduction This report is to test and report on the car manufacturer’s claim that its minivan can get 28 miles per gallon on the highway. The report is based on 35-low milage fleet minivans provided by the manufacturer. First, I will demonstrate Sample mean, Standard Deviation and Confidence interval. To determine if their claim is valid. The second part of report will be based on Hypothesis testing one-tail and two-tail tests. Finally, will give in the conclusion with method of testing was more conclusive. Part 1: Sample Mean, Standard Deviation, and Confidence Interval Calculating the Confidence Interval Data from 35 minivan, highway milage MPG: [ n =35] 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 Using BS2002_M2_resource_ExcelHelper Alpha 0.05 Sample Mean: 26.72 Sample Std Dev: 2.1 n : 35 Margin of Error (Normal Distribution): 0.696 Upper Conf Limit Bound (Normal Distribution): 27.416 Lower Conf Limit Bound (Normal Distribution): 26.024 Margin of Error (t Distribution): 0.721 Upper Conf Limit Bound (t Distribution): 25.999 Lower Conf Limit Bound (t Distribution): 27.441 α = 0.05 µ=26.72mpg σ=2.10 n=35 95% CI [27.416, 26.024] Interpreting the Confidence Interval Page 1 of 4

The 28 MPG claimed by the automobile manufacturer does not fall within the 95% CI. After evaluating the data [ n=35 ] we can determine the UCL and LCL of normal distribution, 95% CI [27.416, 26.024] is not within the plausible value. The UCL [27.416] with [d=0.696] is a plausible value, however, the LCL [26.024] is not plausible at all since it falls short of the parameters. I am confident that there is a 95% probability that the sample population will not be within the manufactures mean, 28 mpg. Part 2: Hypothesis Testing: Two-Tail Test and One-Tail Test Calculating a Two-Tail Test Using BS2002_M1_resource_ExcelHelper Alpha: 0.05 Hypothesized Value: 28 Sample Size: 35 Sample Mean: 26.72 Sample Standard Deviation: 2.10 t -Test Statistic: -3.606 2-Tail t -Test Critical Value: -2.032 t -Test p-value: 0.00100 α = 0.05 t-test statistic = -3.606 H 0 : ≤ 28 H 1 : 28 T-critical value : -2.032 P =0.00100 Interpreting the Two-Tail Test The observed test statistics is in the critical region, therefore the H 0 is rejected. The p-value of 0.001 is less than α (0.05) the indicates that the H 0 is false thus rejecting the null hypothesis. Calculating a One-Tail Test Using BS2002_M1_resource_ExcelHelper Alpha: 0.05 Hypothesized Value: 28 Sample Size: 35 Sample Mean: 26.72 Sample Standard Deviation: 2.10 t -Test Statistic: -3.606 Page 2 of 4

One-Tail t -Test Critical Value: -1.691 t -Test p-value: 0.00000 α = 0.05 t-value = -3.606 H 0 : ≤ 28 H 1 : 28 T-critical value : -1.691 P =0.00 Interpreting the One-Tail Test First, the data independence is met, all ( n=35 ) minivans were randomly selected. The appropriate measurements of the IV and DV were met because the ( DV ) of 28 MPG (H 1 ): µ MPG = 28 µ=26.72mpg σ=2.10 (H 0 ): µ MPG ≤ 28 µ <28 MPG. The null hypothesis is rejected since the t-value is in the critical region. The P value is ≤0 ( α = 0.05), therefore the null hypothesis is rejected. Part 3: Conclusions Methods After evaluating the results of the one-tail test and two-tail test, one can only conclude that the (n=35) tested minivans did not meet the manufacturers claim. Each tested vehicle was randomly chosen, the data was independent of each other. The results show the µ=26.72mpg < 28mpg (manufacturers claim). Therefore, the tested minivans average less than the published 28MPG. Both one and two tail-test rejected the manufactures claim of 28 MPG. The t-Test Statistic is negative the p-Value <0.05 therefore we must reject the H 0 . Even though both rejected the H 0 , the two-tail test offered a more conclusive result since it had the greatest difference from the manufacturer’s claim. The Manufacturer’s Claim I do not support the manufacturers claim. Their publish claim that their minivan get 28 MPG is false advertising. The tests of the 35 tested minivans, indicate that 95% of them will not fall within the manufacturers claim. Summary The tests methods used to collaborate the manufactures claim of 28MPG, I gathered the information form the sample population [n=35]. With this I created the sample mean, standard deviation, and Confidence Interval to determine what percentage of the samples were above and below the sample mean. In this case we wanted to know with certainty if 95% would fall within these parameters. 95% CI [27.416, 26.024]. Then hypothesis testing was performed using the on-tail and two-tail test method. A t-test is performed to determine if the sample mean is significantly different (Carlson & Winquist, 2017), in this case the sample mean of the 35 tested minivan is 26.72mpg. Page 3 of 4

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We need to see if 95% of the tested minivans would fall within the parameters of the manufactures claim, 28mpg. With the hypothesis testing one can see the plausibility of the sample population, whether the 35 minivans mean MPG is different than the 28mpg. In this study we see that in fact the sample mean is not plausible. Which is why the manufacturers claim is rejected. Recommendations My recommendation to the manufacture is for them to claim the 28 MPG but include the SD as well. Then we as consumers will be able to better understand their claim. Currently it is misleading information and could lead to lawsuits. Adding a disclaimer that there is a +/- will leave the consumer with a full disclosure. In the end the consumers need to be reassured that the manufactures claim is correct. Attachments File used to make calculations:  BS2002_M1_Resource_ExcelHelper.xlsx  BS2002_M2_Resource_ExcelHelper.xlsx Page 4 of 4

BS2002_

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