Answered: me people believe that different octane…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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=0.02α=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.

Express the null and alternative hypotheses in symbolic form for this claim. Assume μ¯d=μ1−μ2,μd¯=μ1-μ2, where μ1μ1 is the population mean mileage for Octane 87 and μ2μ2 is the mean mileage for Octane 92.

H0:μ¯dH0:μd¯
H1:μ¯dH1:μd¯
What is the significance level?
α=α=
What is the test statistic? Round to 3 decimal places.
=
What is the pp -value? Round to 5 decimal places.
p=p=
Make a decision.
- Reject the null
- Do not reject the null
What is the conclusion?
- There is not sufficient evidence to support the claim that different octanes produce different miles per gallon.
- There is sufficient evidence to support the claim that different octanes produce different miles per gallon.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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