Tutorial 5

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Tutorial 5
Hypothesis Testing
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Tutorial 5
Question 1
The Tictoc watch company claim that they have 25
of the market share. In a survey of 900 people
some 200 people were found to wear a Tictoc
watch. Use these data to test Tictoc's claim
against the alternative that they have less than
a 25 market share. Solution H0 P .25 HA P
roportion (n30). Since alternative hypothesis i
s less than it is one tailed.
Not told in question the significance level so
use a .05. This gives a critical value of 1.64
5. Note it is negative because you are using the alternative hypothesis. Test statistic Cal
culate sample proportion 200 / 900 0.222
-1.9245 Decision Since 1.9245 cal value of 1.645, reject null hypothesis that
is reject the claim that the company has 25 of
the market.
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Tutorial 5
Question 2
A physician claims that joggers maximal volume
oxygen uptake is greater than the average of all
adults. A sample of 100 joggers has a mean of
40.6 ml/kg and a standard deviation of 6 ml/kg.
If the average of all adults is 36.76 ml/kg, is
there enough evidence to support the physicians
claim at a 0.05? Solution H0 µ 36.76, HA µ
36.76 Critical value Since n 100 (i.e.
30) use normal tables. Alternative hypothesis has
sign so it is one tailed. Question says to use
a .05. So critical value is 1.645. Test stati
stic where 40.6 36.76 6.4
(6 / 10) Decision Since 6.4 1.645, reject
null hypothesis.
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Tutorial 5
Question 3
A building contractor buys wire rods from a given
supplier and from past experience he knows that
the breaking strain of the rods is normally
distributed with mean 200 Kg and a standard
deviation of 25 Kg. An alternative supplier
claims to be able to supply rods of similar
quality at a lower cost, and agrees to give a
sample of 25 such rods to the builder for test
purposes. Amongst these the builder finds a mean
breaking strain of 190 Kg. Use this information
to construct a test of the hypothesis that the
two suppliers produce rods of equal quality
against the one tailed alternative that the new
supplier's rods are inferior. Solution H0 µ
200, HA µ Here you are given both the mean and standard
deviation of the original population (which would
rarely be the case), so use the standard normal
tables, even if nchoice of significance level. If you use 5 then
critical value is -1.645. Test Statistic
Decision The test statistic -2 alue -1.645 is significant So reject H0 in fav
our of HA
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Tutorial 5
Question 4
The Redburn and Flash firelighter companies both
claim to produce the longest burning firelighters
on the market. Samples of 60 Redburn and 70 Flash
firelighters were set alight and their burn times
( in minutes ) were noted, yielding the following
data Company n s ---------------------
------------------------- Redburn 60 25.3 5.6
Flash 70 23.4 7.8 ---------------------
------------------------- Test the hypothesis tha
t there is no difference between the average burn
times of the two types of firelighter. Use the 5
level of significance. Solution Test of equality
of two means H0 µx µy, HA µx ? µy
Critical Value Test of two means with standard de
viations unknown but with large sample sizes so
use the standard normal tables.Two tailed test.
Significance level is .05, Critical value is
?1.96. Test Statistic Decision The t
est statistic 1.61 is not significant
as -1.96 0. No real evidence of difference.
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Tutorial 5
Question 5
A financial controller is considering the
purchase of several cars for the firm's car pool.
A decision must be made between Speedo and Zoomo
cars and, in particular, the maintenance costs'
of these cars must be taken into account. Speedo
cars claim that from a sample of 60 of their cars
the average maintenance cost was 27.50 with a
standard deviation of 3.50. Zoomo cars quoted an
average maintenance cost of 25.70 with a
standard deviation of 5.50, this based on a
sample size of 70. Is their any reason to believe
that Speedo cars are dearer to run than Zoomo
cars? Solution Test of equality of two means H0
µs µz , HA µs µz (s Speedo, z
Zoomo) Critical Value Test of two means with sta
ndard deviations unknown but with large sample
sizes so use the standard normal tables. One
tailed test. Have a choice of significance level.
If you use 5 then critical value is 1.645.
Test Statistic Decision The test statist
ic 2.256 critical value 1.645 is significant
So reject H0 in favour of HA
Speedo is more expensive than Zoomo.
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Tutorial 5
Question 6
100 students from each of two different courses
sat the same test. The 100 students in course A
scored a mean grade of 63 with a standard
deviation of 18,whereas those in course B had a
mean score of 67 with a standard deviation of 15.
Is there any reason to believe that there is a
difference between the students in each of the
courses? Solution Test of equality of two means
H0 µA µB , HA µA ? µB Critical
Value Test of two means with standard deviations
known so use the standard normal tables.Two
tailed test. Have a choice of significance level.
If you use 5 then critical value is ?1.96.
Test Statistic Decision The test stati
stic 1.707 is not significant as -1.96 -1.707 real evidence of difference.
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Tutorial 5
Question 7
In a test of driving abilities, 50 of 150 persons
aged under 30 and 40 of 180 persons aged 30 and
over were classified as poor drivers. Test the
hypothesis, at the 5 level, that the proportion
of poor drivers amongst those under the age of 30
is the same as the corresponding proportion of
drivers in the older age group against the
alternative that it is greater.
Solution H0 PU PO (U under 30, O over 30
)HA PU PO Critical Value Test of equality o
f two proportions so use the standard normal
tables. One tailed test. Significance level is 0.
05 Critical value is 1.645. Test Statistic
Decision The test statistic 2.256 c
ritical value 1.645 is significant
So reject H0 in favour of HA
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Tutorial 5
Question 8
A car manufacturer wishes to determine if there
is a difference in potential demand between urban
and rural customers for a 5 door as opposed to a
4 door model of a particular car. When asked
about their preferences 120 out of 200 urban
customers said they would prefer the 5 door model
whereas 100 out of 170 rural customers preferred
the 5 door model. Test the hypothesis that the
proportion of urban and rural customers that
would prefer the 5 door model is the same.
Solution H0 PU PR (U urban, R rural)
HA PU ? PR Critical Value Test of equalit
y of two proportions so use the standard normal
tables. Two tailed test. Have a choice of signifi
cance level. If you use 5 then critical value
is ?1.96. Test Statistic Decision
As 1.96 not reject H0.