The manufacturer claims that your new car gets 35 mpg on the highway. You suspect that the mpg is less for your car. The 70 trips on the highway that you took averaged 34.8 mpg and the standard deviation for these 70 trips was 5.2 mpg. What can be concluded at the αα = 0.05 level of significance?The test statistic Correct = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)Thus, the final conclusion is that ...The data suggest that the population mean is not significantly less than 35 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is less than 35.The data suggest that the sample mean is not significantly less than 35 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is less than 34.8.The data suggest that the populaton mean is significantly less than 35 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 35.

Given,sample size(n)=70sample mean(x¯)=34.8sample standard deviation(s)=5.2population mean(μ)=35and…

Answered: The manufacturer claims that your new…

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

The manufacturer claims that your new car gets 35 mpg on the highway. You suspect that the mpg is less for your car. The 70 trips on the highway that you took averaged 34.8 mpg and the standard deviation for these 70 trips was 5.2 mpg. What can be concluded at the αα = 0.05 level of significance?

The test statistic Correct = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
Thus, the final conclusion is that ...
- The data suggest that the population mean is not significantly less than 35 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is less than 35.
- The data suggest that the sample mean is not significantly less than 35 at αα = 0.05, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is less than 34.8.
- The data suggest that the populaton mean is significantly less than 35 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 35.

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 + ...

Expert Solution

Step 1

$G i v e n, s a m p l e s i z e (n) = 70 s a m p l e m e a n (\bar{x}) = 34.8 s a m p l e s \tan d a r d d e v i a t i o n (s) = 5.2 p o p u l a t i o n m e a n (μ) = 35 a n d α = 0.05$