STAT 101 Statistic Problems Paper
Mathematics
- 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:
|
Company A |
Company B |
|
|
Mean response time |
7.6 mins |
6.9 mins |
|
Standard deviation |
1.4 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.
- 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 |
A |
B |
C |
D |
E |
F |
G |
|
Before |
9.6 |
9.7 |
9.7 |
9.4 |
9.7 |
9.5 |
9.5 |
|
After |
9.7 |
9.9 |
9.7 |
9.3 |
9.8 |
9.8 |
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.
- 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, x~ = 2,26,450 miles and s=11,500 miles . Use a significance level of
a= 0.01
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Thank you
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