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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