Introductory Statistics 161 Assignment 2 Part A: Analysis of traffic data In this section you will use the data you collected in Assignment 1. Car Size (m^3) Body Year Year 9.941 Small Cars 2003 Less...

Introductory Statistics 161 Assignment 2


Part A: Analysis of traffic data
In this section you will use the data you collected in Assignment 1.
Car Size
(m^3) Body
Year
Year
9.941 Small Cars 2003 Less than 2005
10.251 Small Cars 1996 Less than 2005
10.699 Small Cars 2012 Greater than 2005
9.139

Medium
Cars
1972
Less than 2005
10.426
Medium
Cars
1986
Less than 2005
11.304
Medium
Cars
2001
Less than 2005
12.255
Medium
Cars
2007
Greater than 2005
12.332
Medium
Cars
2007
Greater than 2005
13.305 Large Cars 2004 Less than 2005
13.387 Large Cars 2004 Less than 2005
13.955 Large Cars 2004 Less than 2005
13.402 Large Cars 2011 Greater than 2005
13.470 Large Cars 2011 Greater than 2005
13.484 Large Cars 2010 Greater than 2005
14.618 Luxury Cars 2010 Greater than 2005
14.987 Luxury Cars 2010 Greater than 2005
13.814 Luxury Cars 2002 Less than 2005
14.278 Luxury Cars 2002 Less than 2005

1. Comparing two means:

a) Confidence interval for difference between means [4 Marks]
(i) Use Minitab to construct a 95% Confidence Interval for the difference between
the means of your numeric variable for the different levels of your 2-level categorical
variable.

Two-sample T for Car Size (m^3)
Year N Mean StDev SE Mean
Greater than 200 8 13.16 1.38 0.49
Less than 2005 10 11.98 1.95 0.62
Difference = mu (Greater than 2005) - mu (Less than 2005)
Estimate for difference: 1.17588
95% CI for difference: (-0.55953, 2.91128)
(ii) Interpret your confidence interval in context (remember units).
This analysis provides evidence that the difference between means for car size greater
than 2005 and car size less than 2005 in the population is likely to be between -0.55 and
2.91 m^3.
(iii) Use your confidence interval to draw a conclusion about the difference (if any)
between the two levels of your categorical variable.
The 95% confidence interval is (-0.55, 2.91) which includes zero, thus suggesting that
there is no difference of car size in respect to years.


b) Two-tailed hypothesis test for the difference between two means [4 Marks]
(i) State the null and alternative hypotheses (in words and symbols) for testing if
there is a significant difference between the means of your numeric variable for the
different levels of your 2-level categorical variable.
Let µ1 is the mean of car size for less than 2005 and µ2 is the mean of car size for
greater than 2005.
Null hypothesis
H0: µ1 = µ2 (means of car size are equal for less than 2005 and greater than 2005)
Alternative hypothesis
H0: µ1 ≠ µ2 (means of car size are equal for less than 2005 and greater than 2005)
(ii) Use Minitab to carry out the test. State the test statistic and corresponding p-
value for these hypotheses.

Two-sample T for Car Size (m^3)
Year N Mean StDev SE Mean
Greater than 200 8 13.16 1.38 0.49
Less than 2005 10 11.98 1.95 0.62
T-Test of difference = 0 (vs not =): T-Value = 1.44 P-Value = 0.170 DF = 16
Both use Pooled StDev = 1.7258
(iii) Explain whether you have evidence for or against the null hypothesis.
As the p-value is 0.17, we have evidence for the null...