Question

We are interested in comparing the average maximum pressure for two brands of tyres. A random selection of 25 Goodyear economy tyres had an average maximum pressure of 46.0 psi, with a standard deviation of 6 psi. A random selection of 23 Firestone economy tyres had an average maximum pressure of 50.1 psi with a standard deviation of 4 psi. We can assume that maximum pressure is normally distributed. All hand-calculated steps must be shown.

1a) Clearly state the hypotheses required to compare the average maximum pressure rating for Goodyear and Firestone economy tyres.

1b) Perform the statistical hypothesis testing to test your hypotheses, given a level of significance α = 0.05.

1c) State your full conclusion for the research question.

Note: An Excel Spreadsheet template concluded the two-tailed Test Decision is to REJECT the Null Hypothesis. Please explain why this is the case.

Answer 1

Solution:

Given

n1 = 25 sample size of Goodyear economy tyre

n2 = 23 sample size of Firestone economy tyres.

psi sample mean of Goodyear economy tyres.

psi sample mean of Firestone economy tyres

s1= 6 psi sample standard deviations of Goodyear economy tyres

s2 = 4 psi sample standard deviations of Firestone economy tyres.

level of significance

a )To test the hypothesis

. Vs.

OR

Ho : There is no difference between the average maximum pressure rating for Goodyear and Firestone economy tyres.

Vs

Ha : There is difference between the average maximum pressure rating for Goodyear and Firestone economy tyres.

b ) Test statistic

Where

t = - 2.760002

Test statistic t = - 2.76

At

from t table

The t critical value is 2.013

Decision :

Reject Ho .

c) Conclusion : Reject Ho, there is sufficient evidence to conclude that the average maximum pressure rating for Goodyear and Firestone economy tyres are different.