Question

A study was performed to test whether cars get better fuel consumption on premium petrol than on regular petrol. Each of ten 6-cylinder cars was first filled with either regular or premium, decided by a coin toss, and the fuel consumption for that tank was recorded. The consumption was recorded again for the same cars using the other kind of petrol. A lower fuel consumption figure in litres/100km is better fuel consumption

A second test was conducted using ten 4-cylinder cars and the difference between Regular and Premium fuel consumption for 4 cylinder cars is included in the table below.

Part 1. Consider the information given about the experimental design, and test if fuel consumption in litres/100km is better (ie lower) using premium instead of regular for 6cyl cars?

Define the parameter(s) involved (1 mark)

Parameter is the proportion of 6 cylinder cars/fuel consumption

State the Null and Alternate hypotheses

Ho:

What assumption(s) is/are required to perform this test? (You can assume any required assumptions have been met) (1 mark)

Consider the two charts below. Using the appropriate chart for your test, what is i) the range of the p-value, ii) your decision regarding H₀, and iii) your conclusion about fuel consumption?

Calculate and Interpret a 95% Confidence Interval for the population parameter. The relevant critical value is 2.262

6cyl Car	Regular	Premium	6 cyl Diff = R-P		4cyl Car	4 cyl Diff = R-P
1	15	12	3		1	3
2	12	11	1		2	1
3	11	10	1		3	3
4	11	10	1		4	3
5	10	9	1		5	2
6	11	9	2		6	2
7	9	9	0		7	2
8	9	9	0		8	2
9	9	8	1		9	2
10	8	7	1		10	1
Means	10.5	9.4	1.1			2.1

Answer 1

For 6Cyl Car:

Std Error of Diff(se) = Std Dev/n^1/2 = 0.277

Alpha = 0.05

Null and Alternate Hypothesis:

H0: Mean of Premium is same as Mean of Regular

Ha: Mean of Regular is greater than Mean of Premium

Test Statistic:

t = Diff of Means /SE of Difference = 1.1/0.277 = 3.97

Degrees of Freedom = n-1 = 10-1 = 9

p-value = TDIST(3.97,9,1) = 0.001621

Result:

At alpha = 0.05, Since the p-value is less than 0.05, Hence we reject the null hypothesis.

Conclusion:

Mean of Regular is greater than Mean of Premium ie 6 Cycl Cars get better fuel consumption when using Premium petrol than Regular Petrol (Low value of Mean signifies better fuel efficiency)

Assumptions of paired t-test

• The dependent variable must be continuous.

• The observations are independent of one another.

• The dependent variable should be approximately normally distributed.

• The dependent variable should not contain any outliers.