Answered: Fueleconomy.gov, the official US…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage (city and highway combined) in miles per gallon (MPG) from 22 users who drive a 2008 Nissan Sentra (2WD). Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed.

Nissan Sentra (2WD) from fueleconomy.gov

Average MPG

Mean

29.41

Standard Error

0.863153773

Median

30.15

Mode

27.8

Standard Deviation

4.05

Sample Variance

16.39075758

Kurtosis

0.08349459

Skewness

-0.663433157

Range

15.4

Minimum

19.8

Maximum

35.2

Sum

647.1

Count

Confidence Level (95.0%) Margin of error t dist

1.80

The EPA claims the 2008 Nissan Sentra gets 28MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? The hypotheses for the test are:

Ho: μ = 28
Ha: μ ≠ 28

Using a t distribution test, conduct the t-test. There are __________ degrees of freedom (n-1).

Use Excel to get the test statistic & p-value and submit the Excel file:

The test statistic is: __________________ (please round to two decimal places)

The p-value for this hypothesis test is: __________________ (please round to four decimal places)
Tip: P-values are probabilities, so they are from 0 to 1. In Excel use T.DIST to look up the probability and if it is a two tailed t-test you can use the .2t version or simply multiply by 2 in the regular version =2*T.DIST(-|test statistic|,n-1,TRUE) or =T.DIST.2T(test statistic,n-1)

The conclusion for the hypothesis test is:

Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we accept the null hypothesis
Since p ≥ α we reject the null hypothesis and accept the alternative

(c) Calculate a 95% confidence interval for the average gas mileage of a 2008 Nissan Sentra by drivers who participate on fueleconomy.gov.

CAUTION: The =CONFIDENCE.T functions in Excel provide you with the margin of error, you still have to then subtract from and add to the sample statistic (mean or other) to get the confidence interval lower and upper limits.

We are _______ % confident that the true population gas mileage of a 2008 Sentra by drivers who participate on fueleconomy.gov is between ______________ mpg and ___________ mpg. (please round to two decimal places if needed)

Recall that the t uses the same pattern as the z in computation so you can do it by hand or use =STANDARDIZE in Excel with the same values needed to do it by hand.

Z or t-test test statistic computation

= sample statistic – hypothesized value all divided by standard error

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

Expert Solution