Question

A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately

1

2

mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers.

Amount by Which Speed Limit Was Exceeded

Male Driver	Female Driver
1.4	-0.2
1.2	0.5
0.9	1.1
2.1	0.7
0.7	1.1
1.3	1.2
3	0.1
1.3	0.9
0.6	0.5
2.1	0.5

(a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μ_males − μ_females. Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.)

t	=
df	=
P	=

(b) Do these data provide convincing support for the claim that, on average, male teenage drivers exceed the speed limit by more than do female teenage drivers?

YesNo    

Answer 1

Working

We find the mean, variance and standard deviation of the data using Excel functions average, var.s and stdev.s respectively.

	n	Mean (M)	Variance (SS)	Standard Deviation (SD)
Males	n1 = 10	M1 = 1.46	SS1 = 0.5493	s1 = 0.7412
Females	n2 = 10	M2 = 0.64	SS2 = 0.2071	s2 = 0.4551

The null and alternative hypotheses are
Ho :  μmales = μfemales
Ha :  μmales > μfemales
where μ_males and μ_females are population means for exceeding speed limits of males and females respectively.

α = 0.01

We use independent Samples T test since population standard deviation is unknown, and sample size is small
Using the given formulae, we get

Degrees of Freedom
df1 = n1 - 1 , df2 = n2 - 1 , df = n1 + n2 - 2

df = 18

Pooled Variance

Sp² = 0.3782

Mean Squared Error S_m1-m2

S_m1-m2 = 0.275

t-statistic

t-statistic = t = 2.9814

P-value
For t = 2.9814, df = 18 we find the one tailed p-value using t tables or Excel function t.dist
p-value = 1 - t.dist(2.9814, 18, TRUE)
p-value = 0.004

Answer :

t	=	2.98
df	=	18
P	=	0.004

b)

Decision
0.004 < 0.01
that is p-value is less than alpha.
Hence we Reject Ho.

Answer :

YES
The data provides convincing support at α = 0.01 to show that on average, male teenage drivers exceed the speed limit by more than do female teenage drivers.