Question

Data on petrol prices was collected for the Royal Automobile Club of Queensland by FuelTrac Pty Ltd. The data was collected in Toowoomba, Queensland over a nine month period from September 2002 to May 2003 with the aim of investigating complaints about excessive price differences between lead replacement petrol and unleaded petrol.

The data are monthly average fuel prices. There are nine observations on three variables.

Month The month

Unleaded The monthly average price of unleaded petrol (in cents per litre)

LRP The monthly average price of lead replacement petrol (LRP) (in cents per litre)

For each month the difference in prices is calculated and the values are shown in the table below:

Month Diff

Sep 3.4

Oct 3.6

Nov 3.7

Dec 3.8

Jan 3.9

Feb 3.7

Mar 3.8

Apr 4

May 4

You may assume that the differences in prices is normally distributed. Some computer output appears below:

One Variable Summary. Unleaded LRP Dif

Mean 85.278 89.044 3.7667
Std. Dev. 4.845 4.893 0.1936
Count 9 9 9

a) Is the lead replacement petrol more expensive than unleaded petrol? Explain why or why not? Your answer should be in the form of a hypothesis test. Justify any assumptions that need to be made in order for your results to be reliable.

b) Construct a 95% confidence interval for the average price difference between lead replacement petrol and unleaded petrol.

Answer 1

A.

Note :- (LRP= lead replacement petrol,ULP=unleaded petrol)

Hypothesis to be tested is : Price of LRP > Price of ULP

H0:

Let d=0 and asume there is no difference between prices of LRP & ULP

v/s

H1: Not H0

Test statistic :

t = [ () ] / SE

= 1.6669

where

is the mean of LRP, Mean of LRP= 89.044

is the mean of ULP,Mean of ULP=85.278

d is the hypothesized difference , D=3.7667

SE is the standard error.

To calculate Standard error (SE):

SE = sqrt[ (s12/n1) + (s22/n2) ] = 2.2592

where

s1 is the standard deviation of LRP =4.893

s2 is the standard deviation of ULP= 4.845

n1 is the size of LRP, and n2 is the size of ULP. = 9

Probability value of P(t<1.6669) =0.9330

At 95% C.I p-value is greater than 0.05 hence we reject the null hypothesis that prices of LRP & ULP is same.

LRP seems to be more expensive than ULP considering mean provided.

B.

Lower Limit = -(tCL)() = -0.661332
Upper Limit = +(tCL)() = 8.265292

where tCL is 1.96 at 95 % C.I