Question 1
Motor vehicles have a recommended tire pressure of 32 psi (pounds per square inch). The
road safety authority launches a roadside checkpoint to measure the actual tire pressure in the
front left tire of a random sample of 50 passing cars. The authority hopes to use this
information to decide whether an additional investment in air pumps is required at filling
stations.
(a) Define the population characteristic of interest in the above example. (2 marks)
(b) The following SPSS output has been produced from a one sample t-test. Using the 5-step
approach to hypothesis testing, determine whether the road safety authority should invest in
additional air pumps at filling stations. (10 marks)
One-Sample Statistics
N Mean
Std.
Deviation Std. Error Mean
Tire pressure 50 32.8200 1.98659 .28095
One-Sample Test
Test Value = 32
t df
Sig.
(2-tailed)
Mean
Difference
95% Confidence Interval of
the Difference
Lower Upper
Tire pressure 2.919 49 .005 .82000 .2554 1.3846
(c) The following 95% confidence interval has been computed for the mean tire pressure of
all motor vehicles. Does the confidence interval support the conclusion you made in part (b)?
Explain your answer in detail. (4 marks)
(d) Assume that the median tire pressure of all motor vehicles is 32.82. Produce an
appropriate graph that gives an approximation of the likely distribution of the tire pressure
variable. (3 marks)
(Note: You may use insert: shapes: lines: freeform scribble or manually sketch the graph and
insert a photographic image of the graph in your word solution document.)
(e) Redraw the graph assuming that the median tire pressure of all motor vehicles is actually
34. (3 marks)
(f) Comment on the graph in part (e) and provide an example of a dataset that would likely
follow a similar distribution.
