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# QMET 352- Exam 1 Study Guide QMET 352

University of Louisiana at Lafayette

GPA 3.9

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This 3 page Study Guide was uploaded by Alexandra Casey on Saturday January 30, 2016. The Study Guide belongs to QMET 352 at University of Louisiana at Lafayette taught by Dr. John Tanner in Spring 2016. Since its upload, it has received 557 views. For similar materials see Advanced Business Statistics in Business at University of Louisiana at Lafayette.

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Date Created: 01/30/16

t-Test: Two-Sample Assuming Equal Variances Sample Call Population Time Mean QMET 352 REFERENCE SHEET/ Study Guide Mean 219.6666667 240 Variance 3316.424242 0 EXAM 1 (80PTS): 75 MINUTES,5 QUESTIONS, Observations 12 12 Pooled Variance 1658.212121 and 15 MINUTES PER QUESTION Hypothesized Mean Difference 0 df 22 ONE SET OF SAMPLE DATA Example : 3) - A telemarketing company located in Los Angeles t Stat 1.223106186 established a guideline that states that the average time P(T<=t) one-tail 0.117115037 t Critical one-tail 1.321236742 for each completed call should be 4 minutes or less. P(T<=t) two-tail 0.234230075 Recently, the operations manager was concerned that t Critical two-tail 1.717144374 calls were taking too long, but he did not want to present this material to his callers if the sample data did not significantly support him. A sample of 12 recent calls was selected, and the following times (in seconds) were recorded: 194, 278, 302, 140, 245, 234, 268, 208, 102, 190, 220, 255 Using the .10 level of significance, what should the operations manager conclude? 1. What is a Null Hypothesis (H )?*0 Never include numbers. Ex: There is no significant difference between the average time it takes to complete a telemarketing call according to company guidelines and the average time it took in the sample. 2. How many tails does this problem have? 1-tail test (less than, more than, higher, lower, etc.) 2-tail test means are EXACTLY the same or not? Ex: This problem has only one tail since it states 4 minutes or less. 3. What is the level of significance? Level of significance (Risk Factor/ L of S/ α- alpha symbol): the percent chance we are willing to take that our conclusions might be wrong Ex: 0.10 compare to p-value for ACR i. Table value? Use t-critical 1. ANY 2-tail test must put +/- (±) sign in answer 2. 1-tail test put EITHER + or – Ex: t-critical/ Table Value= -1.321 (this is negative because the sample mean is smaller than the population mean) 4. What is the ACR statement? (Action, Conclusion, Recommendation) NEVER USE THE WORDS “significant” or “difference” IN ACR i. As long as your recommendation makes sense, you are fine. P-value- P (T<=t) Ex: A: Accept the null hypothesis: the p-value is greater than the level of significance 0.117 > 0.10 C: It appears that the company calls are meeting company guidelines. R: Continue calls the same way. TWO SETS OF SAMPLE DATA Example: 1) Technology has done more to change the sport of golf than possibly any other sport in recent times. Titanium woods and irons and new golf ball designs have t-Test: Paired Two Sample for Means Existing New Ball impacted professional and amateur golfers alike. A Ball(yds) (yds) maker of golf balls has developed a new ball Mean 286.833333 289 technology, and is interested in determining whether Variance 178.966667 161.2 this new ball will result in increased driving distances. Observations 6 6 To help determine this, the manufacturer selected six Pearson Correlation 0.94553356 professional golfers and had each golfer drive the existing ball once, and then drive the new ball once. Hypothesized Mean Difference 0 The results are as follows: df 5 t Stat -1.218631 Golfer Existing Ball(yds) New Ball (yds) P(T<=t) one-tail 0.1386699 1 278 285 2 299 301 t Critical one-tail 2.01504837 3 280 276 P(T<=t) two-tail 0.2773398 4 295 300 t Critical two-tail 2.57058184 5 268 273 6 301 299 Using an alpha level of .05, what can be concluded about the effectiveness of the new ball technology, with respect to driving distance? What kind of t-test is this? 1. What kind of t-test is this? Ex: This is a paired sample test due to the fact that the same six professional golfers hit the existing ball and the new ball. So we will run the t-Test for Paired Two Sample for Means. 2. What is a Null Hypothesis (H )0 Ex: There is no significant difference between the average driving distance the golfers got with the existing ball and when they hit the new ball. 3. How many tails does this problem have? 1-tail tes (less than, more than, higher, lower, etc.) 2-tail tes means are EXACTLY the same or not? Ex: This problem has only one tail since it states a test ofincreased driving distance. 4. What is the level of significance? Level of significance(Risk Factor/ L of S/ α- alpha symbol): the percent chance we are willing to take that our conclusions might be wrong Ex: 0.05 compare to p-value for ACR i. Table value? Use t-critical 1. ANY 2-tail test must put +/- (±) sign in answer 2. 1-tail test put EITHER + or – Ex: t-critical/ Table Value= -2.02 (this is negative because the new ball mean is smaller than the existing ball mean) 5. What is the ACR statement? (Action, Conclusion, Recommendation) NEVER USE THE WORDS “significant” or “difference” IN ACR i. As long as your recommendation makes sense, you are fine. P-value- P (T<=t) Ex: A: Accept the null hypothesis: the p-value is greater than the level of significance 0.14 > 0.05 C: It appears that the driving distance of the new ball is the same as the existing ball. R: Improve the technology for the new golf ball. TWO SETS OF SAMPLE DATA Example: 2) The State College registrar is interested in determining whether there is a difference between the number of credit hours taken by female and male students. In a random sample of sixty males and sixty females, the following statistics were calculated: Males_______ Females______ If the Excel p-value for this problem is Means 13.24 credit hrs 14.65 credit hrs 0.0003 and the .05 level of significance is to be used, what would Standard 1.20 credit hrs 1.56 credit hrs Deviations you tell the registrar? 1. What kind of t-test is this? Ex: This is an independent sample test due to the fact that it is two random samples of men and women. 2. What is a Null Hypothesis (H )0 Ex: There is no significant difference between the average number of credit hours taken by female and male students at the state college. 3. How many tails does this problem have? 1-tail tes (less than, more than, higher, lower, etc.) 2-tail tes means are EXACTLY the same or not? Ex: This problem has two tails since it does not specify what we are looking for in the problem. 4. What is the level of significance? Level of significance(Risk Factor/ L of S/ α- alpha symbol): the percent chance we are willing to take that our conclusions might be wrong Ex: 0.05 compare to p-value for ACR i. Table value? Use t-critical Ex: We are not given a table for this problem, thus we do not have a table value/ t-critical. It is not needed because the p-value is given and we can base the ACR off of the comparison of the p-value and the level of significance. 5. What is the ACR statement? (Action, Conclusion, Recommendation) NEVER USE THE WORDS “significant” or “difference” IN ACR i. As long as your recommendation makes sense, you are fine. P-value- P (T<=t) Ex: A: Reject the null hypothesis: the p-value is less than the level of significance 0.0003 < 0.05 C: It appears that female students take more credit hours than male students at the state college. (Only when you reject do you look at the numbers reasonably/ visually) R: Encourage more men to register for more credit hours.

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