STAT 101 Saudi Assign 3 Temperature Measurements Statistics Questions

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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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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:
̅ (sample mean) = 20ºC
𝒙
σ=1.5ºC
population mean = 22ºC
n = 40
α = 0.05
H0 : ...

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