12 questions need to be fully solved please see the attached paper
assignment_3_stat101_2nd_2018_19.docx

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CSTS-SEU-KSA
___________________________________________________________________
Statistics (STAT-101)
Assignment-3 (Weeks: 9-11)
2nd Semester, 1439-1440 (2018-2019)
Student’s Name
Student’s ID
Section/CRN
Location
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:
CSTS-SEU-KSA
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:
CSTS-SEU-KSA
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:
7 Find the best predicted systolic blood pressure in the left arm given that the systolic blood
pressure in the right arm is 100 mm Hg (using Regression line).
Right Arm
Left Arm
Solution:
102
175
101
169
94
182
79
146
79
144
CSTS-SEU-KSA
8 Find the Linear correlation coefficient between the blood pressure in right arm (x) and the
blood pressure in left arm (y) using the data given in Question 1.
Solution:
9 Winning team data were collected for teams in different sports, with the results given in
the table
Home team wins
Visiting team wins
Total
Baseball
53
47
100
Hockey
50
43
93
Football
57
42
99
Total
160
132
292
Use a 0.05 level of significance to test the claim that home/visitor wins are independent of
the sport. Given that the critical value of 2 for 2 d.f. = 5.991.
Solution:
10 The observed frequencies of sales of different colors of cars are shown in the following
table:
Car Color
BLACK
BLUE
GREEN
RED
WHITE
Total
Observed Frequencies
12
8
14
6
10
50
A manager of a car dealership claims that the probabilities of sales of different colors are
equal.
Compute the 𝜒 2 test statistic and test the manager’s claim of equal probabilities of different
colors at 5% level of significance [Given that 𝜒0.05 2 (4 𝑑. 𝑓. ) = 9.49].
CSTS-SEU-KSA
Solution:
11 While conducting a one-way ANOVA comparing 4 treatment samples with 7 observations
per treatment sample, computed value for SS(Total) = 60 and MS(Treatment) = 4.
Construct the ANOVA table and find the value of F.
Solution:
12 Given the sample data below, find the F -test statistic value
𝑛
Mean
Variance 𝑠 2
Solution
Sample 1
4
2.0
0.75
Sample 2
4
3.0
1.00
Sample 3
4
4.0
1.25

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