Questions: Some people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane. Person Miles with 87 Octane Miles with 92 Octane --------- 1 234 237 2 257 238 3 243 229 4 215 224 5 114 119 6 287 297 7 315 351 8 229 241 9 192 186 10 204 209 11 547 562 Do the data support that different octanes produce different miles per gallon at the α=0.02 level of significance? Note: A normal probability plot of difference in car mileage between Octane 87 and Octane 92 indicates the population could be normal and a boxplot indicated no outliers. a. Express the null and alternative hypotheses in symbolic form for this claim. Assume µd̄=µ1−µ2, where µ1 is the population mean mileage for Octane 87 and µ2 is the mean mileage for Octane 92. H0: µd̄ = 0 H1: µd̄ ≠ 0 b. What is the significance level? α= 0.02 c. What is the test statistic? Round to 3 decimal places. ? d. What is the p-value? Round to 5 decimal places. p= e. Make a decision. - Reject the null - Do not reject the null f. What is the conclusion? - There is sufficient evidence to support the claim that different octanes produce different miles per gallon. - There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.
Transcript text: Some people believe that different octane gasoline result in different miles per gallon in a vehicle. The following data is a sample of 11 people which were asked to drive their car only using 10 gallons of gas and record their mileage for each 87 Octane and 92 Octane.
Person | Miles with 87 Octane | Miles with 92 Octane
---|---|---
1 | 234 | 237
2 | 257 | 238
3 | 243 | 229
4 | 215 | 224
5 | 114 | 119
6 | 287 | 297
7 | 315 | 351
8 | 229 | 241
9 | 192 | 186
10 | 204 | 209
11 | 547 | 562
Do the data support that different octanes produce different miles per gallon at the $\alpha=0.02$ level of significance? Note: A normal probability plot of difference in car mileage between Octane 87 and Octane 92 indicates the population could be normal and a boxplot indicated no outliers.
a. Express the null and alternative hypotheses in symbolic form for this claim. Assume $\mu_{\bar{d}}=\mu_{1}-\mu_{2}$, where $\mu_{1}$ is the population mean mileage for Octane 87 and $\mu_{2}$ is the mean mileage for Octane 92.
\[
\begin{array}{l}
H_{0}: \mu_{\bar{d}} = 0\\
H_{1}: \mu_{\bar{d}} \neq 0
\end{array}
\]
b. What is the significance level?
$\alpha= 0.02$
c. What is the test statistic? Round to 3 decimal places.
? $\square$
d. What is the $p$-value? Round to 5 decimal places.
$p=$ $\square$
e. Make a decision.
- Reject the null
- Do not reject the null
f. What is the conclusion?
- There is sufficient evidence to support the claim that different octanes produce different miles per gallon.
- There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.
Solution
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