CPMP and Word Problems

10. CPMP and word problems µ1 = CPMP students Hypotheses: H0: µ1 – µ2 = 0 HA: µ1 – µ2 ≠ 0 df  590 t590  µ2 = traditional students 57.4  53.9 2 2  1.406 32.1 28.5  320 273 P  Value  2P( t590 | 1.406 |)  0.160 Conclusion: Since the P-Value is greater than alpha(0.160 > 0.05) we fail to reject the null hypothesis. There is not enough evidence to state that there is a difference in the mean test scores between students in CPMP and traditional Math programs. 1. 2. 3. 4. Interpret the P-Value in context. Describe Type I error in context. Describe Type II error in context Describe Power in context. 1. There is a 16% chance of getting a difference in sample means of 3.5 points or one more extreme if there really is no difference in the mean scores for students in CPMP and Traditional classes. 2. We state that there is a difference in the mean scores of students in the CPMP and Traditional classes but there is not a difference. 3. We state that there is not a difference in the mean scores of students in the CPMP and Traditional classes but there is a difference. 4. The probability we state that there is a difference in the mean scores of students in the CPMP and Traditional classes and there is a difference. 14. Egyptians – Test if there is evidence that there was a change in the average skull breadth between the two time periods µ1 = average skull breadth for 4000 B.C.E. µ2 = average skull breadth for 200 B.C.E. Hypotheses: H0: µ1 – µ2 = 0 HA: µ1 – µ2 ≠ 0 Conditions: Random: Not random but we will assume the are representative samples 10% Condition: 30 skulls is less than 10% of all skulls of Egyptian males from 4000 B.C.E. and 200 B.C.E. Independence: It is safe to assume that the skull sizes would be independent between the two ages Nearly Normal condition: Both Normal Probability Plots show approximately linear forms(also both samples are large) 4000 BCE 200 BCE All conditions have been met to use Student’s t-model for a 2 sample t-test. µ1 = average skull breadth for 4000 B.C.E. µ2 = average skull breadth for 200 B.C.E. Hypotheses: H0: µ1 – µ2 = 0 HA: µ1 – µ2 ≠ 0 x1  131.37 s1  5.13 n1  30 x2  135.63 s2  4.04 n2  30 df  54.97 t55  131.37  135.63 5.132 4.042  30 30  3.580 P  Value  2P  t 55 | 3.580 |   0.00073 Conclusion: Since the P-Value is less than alpha(0.00073<0.05), we reject the null hypothesis. There is statistically significant evidence that there is a difference in the average skull breadth between 4000 B.C.E. and 200 B.C.E. Sentences – Using #14 a. What does P-Value mean in context There is a 0.073% chance of getting a difference in sample means of 4.26 mm or one more extreme if there is no difference in the skull breadth between male Egyptians from 4000 BCE and 200 BCE. b. Type I error We state there is a difference in the skull breadth of male Egyptians from 4000 BCE and 200 BCE but there really is no difference c. Type II Error We state there is no difference in the skull breadth of male Egyptians from 4000 BCE and 200 BCE but there really is a difference d. Power The probability we state there is a difference in the skull breadth of male Egyptians from 4000 BCE and 200 BCE but there really is a difference e. 95% confidence About 95% of differences in the sample means from random samples of these populations will produce confidence intervals that contain the true difference in skull breadth 95% Confidence interval: All conditions have been met to use Student’s t-model for a 2 sample t-interval Mechanics: x1  1631.59 s1  138.470 n1  34 x2  1388.85 s2  151.114 n2  27 df  54.97  t55  2.004 5.132 4.042 CI : 131.37  135.63   2.004  30 30  6.655, 1.878  Conclusion: We are 95% confident that the true mean skull breadth of Egyptian Males from 4000 B.C.E is between 6.655mm to 1.878mm smaller than Egyptian Males from 200 B.C.E.