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CSTS-SEU-KSA

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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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