Martin Motors has in stock three cars of the same make and model. The Sales Mana
ID: 3150647 • Letter: M
Question
Martin Motors has in stock three cars of the same make and model. The Sales Manager would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.
Martin Motors has in stock three cars of the same make and model. The Sales Manager would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.
Explanation / Answer
Martin Motors has in stock three cars of the same make and model. The Sales Manager would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.
Distances in miles
Types of Gasoline
Car A
Car B
Car C
Regular
28.1
24
29.2
Super regular
24.1
22.5
26.4
Unleaded
23.5
26.5
23
Premium unleaded
25
24.5
26.3
Here, we have to use the chi square test for the independence between the distances in miles and the types of Gasoline. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The two categorical variables distances in miles and types of gasoline are independent.
Alternative hypothesis: H0: The two categorical variables distances in miles and types of gasoline is not independent.
The test statistic formula is given as below:
Chi-square = [(O – E) ^2 / E]
The chi square test for independence is given as below:
Chi-Square Test
Observed Frequencies
Distances in miles
Types of Gasoline
Car A
Car B
Car C
Total
Regular
28.1
24
29.2
81.3
Super regular
24.1
22.5
26.4
73
Unleaded
23.5
26.5
23
73
Premium unleaded
25
24.5
26.3
75.8
Total
100.7
97.5
104.9
303.1
Expected Frequencies
Distances in miles
Types of Gasoline
Car A
Car B
Car C
Total
Regular
27.01059
26.15226
28.13715
81.3
Super regular
24.25305
23.48235
25.2646
73
Unleaded
24.25305
23.48235
25.2646
73
Premium unleaded
25.18331
24.38304
26.23365
75.8
Total
100.7
97.5
104.9
303.1
Data
Level of Significance
0.05
Number of Rows
4
Number of Columns
3
Degrees of Freedom
6
Results
Critical Value
12.59159
Chi-Square Test Statistic
0.970521
p-Value
0.986705
Do not reject the null hypothesis
Expected frequency assumption
is met.
Here, we get the p-value as 0.9867 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the two categorical variables distances in miles and types of gasoline are independent.
Distances in miles
Types of Gasoline
Car A
Car B
Car C
Regular
28.1
24
29.2
Super regular
24.1
22.5
26.4
Unleaded
23.5
26.5
23
Premium unleaded
25
24.5
26.3
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