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CSTS-SEU-KSA
___________________________________________________________________
Statistics (STAT-101)
Assignment-3 (Weeks: 9-11)
2nd Semester, 1439-1440 (2018-2019)
Due date: 30/03/2019 (Time 11 PM )
Student’s Name
Student’s ID
Section/CRN
Location
Marking Scheme
Question
Score
Q-1
3
Q-2
3
Q-3
3
Q-4
3
Q-5
3
Q-6
3
Total
18
Obtained Score
CSTS-SEU-KSA
1. Various temperature measurements are recorded at different times for a particular city. The
mean of 20ºC is obtained for 40 temperatures on 40 different days. Assuming that σ=1.5ºC,
test the claim that the population mean is 22ºC. Use a 0.05 significance level.
Identify the null hypothesis, alternative hypothesis, test statistics, P-value and final the
conclusion about the original claim.
Solution:
2. A random sample of 16 women resulted in blood pressure levels with a standard deviation of
22.7 mm Hg. A random sample of 17 men resulted in blood pressure levels with a standard
deviation of 20.1 mm Hg.
Use a 0.05 significance level to test the claim that blood pressure for women vary more than
blood pressure levels for men.
Solution
3. A manufacturer considers his production process to be out of control when defects exceed
3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this
is only a sample fluctuation and production is not really out of control. Identify the null
hypothesis, alternative hypothesis, test statistics, P-value and At the 0.01 level of significance
, test the manager claim.
Solution:
CSTS-SEU-KSA
4. A researcher was interested in comparing the response times of two different cab companies.
Companies A and B were each called at 50 randomly selected times. The calls to company A
were made independently of the calls to company B. The response times for each call were
recorded. The summary statistics were as follows:
Mean response time
Standard deviation
Company A
7.6 mins
1.4 mins
Company B
6.9 mins
1.7 mins
Use a 0.01 significance level to test the claim that the mean response time for company A is the
same as the mean response time for company B. Use the P-value method of hypothesis testing.
Solution:
5. A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and
their competition scores were recorded before and after the training. The results are shown
below
Subject
Before
After
A
9.6
9.7
B
9.7
9.9
C
9.7
9.7
D
9.4
9.3
E
9.7
9.8
F
9.5
9.8
G
9.5
9.3
Using a 0.01 level of significance, test the claim that the training technique is effective in
raising the gymnasts’ score.
Use the traditional method of hypothesis testing with critical value t= -3.143.
Solution:
6. Test the claim that the mean lifetime of car engines of a particular type is greater than
2,20,000 miles. Sample data are summarized as n=23, 𝑥̅ = 2,26,450 miles and s = 11,500
miles. Use a significance level of  = 0.01
Solution:

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