Final Exam (EC315)

Final Exam (EC315) - PART I HYPOTHESIS TESTING PROBLEM 1 A...

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PART I. HYPOTHESIS TESTING PROBLEM 1 A certain brand of fluorescent light tube was advertised as having an effective life span before burning out of 4000 hours. A random sample of 84 bulbs was burned out with a mean illumination life span of 1870 hours and with a sample standard deviation of 90 hours. Construct a 95 confidence interval based on this sample and be sure to interpret this interval. Answer Since population standard deviation is unknown, t distribution can be used construct the confidence interval. The 95% confidence interval is given by /2, 1 1 , nn SS X t X t       Details Confidence Interval Estimate for the Mean Data Sample Standard Deviation 90 Sample Mean 1870 Sample Size 84 Confidence Level 95% Intermediate Calculations Standard Error of the Mean 9.819805061 Degrees of Freedom 83 t Value 1.988959743 Interval Half Width 19.53119695 Confidence Interval Interval Lower Limit 1850.47 Interval Upper Limit 1889.53
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2 PROBLEM 2 Given the following data from two independent data sets, conduct a one-tail hypothesis test to determine if the means are statistically equal using alpha=0.05. Do NOT do a confidence interval. n 1 = 35 n 2 = 30 xbar 1 = 32 xbar 2 = 25 s 1 =7 s 2 = 6 Answer H0:μ1=μ2 H1: μ1>μ2 Test statistics used is 11 1 2 1 2 2 12 ~ nn X X n n tt S n n  where 22 1 1 2 2 ( 1) ( 2 n S n S S Decision rule : Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value. Details t Test for Differences in Two Means Data Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 35 Sample Mean 32 Sample Standard Deviation 7 Population 2 Sample Sample Size 30 Sample Mean 25 Sample Standard Deviation 6 Intermediate Calculations Population 1 Sample Degrees of Freedom 34 Population 2 Sample Degrees of Freedom 29 Total Degrees of Freedom 63 Pooled Variance 43.01587 Difference in Sample Means 7 t Test Statistic 4.289648 Upper-Tail Test Upper Critical Value 1.669402 p -Value 3.14E-05 Reject the null hypothesis Conclusion: Reject the null hypothesis. The sample provides enough evidence to support the claim that means are different.
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3 PROBLEM 3. A test was conducted to determine whether gender of a display model affected the likelihood that consumers would prefer a new product. A survey of consumers at a trade show which used a female spokesperson determined that 120 of 300 customers preferred the product while 92 of 280 customers preferred the product when it was shown by a female spokesperson.
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This note was uploaded on 08/29/2011 for the course EC 315DLB taught by Professor Randallbarcus during the Fall '10 term at Park.

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Final Exam (EC315) - PART I HYPOTHESIS TESTING PROBLEM 1 A...

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