Statistics

gibonwa33 · #1 $Old$ November 22nd, 2008, 09:13 AM

A large oil company recently conducted a survey amongst motorists to find out their preference among five leading brands of petrol:

Brand preferred...Number of motorists
Caltex ......................118
BP .............................92
Shell ........................135
Trek ..........................88
Engen ......................102

Test the hypothesis that the preference is uniform over the five brands of fuel at the 0.01 level of significance.

CaptainBlack · #2 $Old$ November 22nd, 2008, 11:04 AM

Quote:

Originally Posted by gibonwa33 $View Post$

A large oil company recently conducted a survey amongst motorists to find out their preference among five leading brands of petrol:

Brand preferred...Number of motorists
Caltex ......................118
BP .............................92
Shell ........................135
Trek ..........................88
Engen ......................102

Test the hypothesis that the preference is uniform over the five brands of fuel at the 0.01 level of significance.

You will be doing a $\chi ^2$ test goodness of fit test. The null hypothesis is that there is no difference in preference, and so as the total number of observations is 535, the expected frequencies for each brand are all 107.

So We have a table:

Code:

O(bserved)   E(xpected)
118          107
 92          107
135          107
 88          107
102          107

Then:

$\chi^2=\sum_{i=1}^5 \frac{(O_i-E_i)^2}{E_i}$

and we have 4 degrees of freedom.

You will need to look up the p-value for the value of $\chi^2$ in a table to complete the test.

CB