Assignment-3 (Weeks: 9-11)
2nd Semester, 1439-1440 (2018-2019)
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.
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.
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.
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
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.
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
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.
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
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).
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.
9 Winning team data were collected for teams in different sports, with the results given in
Home team wins
Visiting team wins
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.
10 The observed frequencies of sales of different colors of cars are shown in the following
A manager of a car dealership claims that the probabilities of sales of different colors are
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].
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.
12 Given the sample data below, find the F -test statistic value
Variance 𝑠 2
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