HW10NHSTTwoMeanshertribm

1 ENED 3061 Probability & Statistics HW 10: NHST Two Means - p. Spring 2023, Murphy due by 8:00AM on Thursday April 6 Save this Word document as HW10_NHST_TwoMeans_UCusername , where UCusername is the character string that goes at the beginning of your @mail.uc.edu email address. Submit your completed work (as a Word doc or PDF) to the HW 10: NHST Two Means link in Canvas. Either type your work and answers or include pictures of your hand-written work (make sure it's legible and well organized). Note: This is an individual assignment. The work you submit must be your own. Your submission of work for this assignment indicates your affirmation of the CEAS Honor Code statement, which is provided verbatim below. https://ceas.uc.edu/about/info-current-students/academic-action-criteria.html College of Engineering and Applied Science Honor Code As students of the University of Cincinnati's College of Engineering and Applied Science, we honor the high standards required by our future profession. We pledge to uphold those high standards by practicing integrity within our classrooms, our communities, and our careers. We believe in honest representation of individual work and in fair advancement of academic position; therefore, we refuse to partake in actions at the expense of our academic integrity. We expect academic integrity from our peers who share the responsibilities of this code. Our commitment to this pledge entitles us to trust from our peers, our instructors, and our institution. We maintain the right and share the responsibility to report any unfair advantage with anonymity and without retribution. I hereby affirm that this is my own work in accordance with the Honor Code of the University of Cincinnati College of Engineering and Applied Science.

2 ENED 3061 Probability & Statistics HW 10: NHST Two Means - p. Spring 2023, Murphy due by 8:00AM on Thursday April 6 Complete the following two problems. You can either (a) type in this document or (b) print the document, write your answers by hand, and submit a legible scan. (1) Modification of textbook exercise 5-23. Note that the data are already in the file, MRH5e_Chapter5_exercises_part1.csv , and use Minitab for step 6 (computations). Include your Minitab output in your solutions. Problem Statement : In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic in this process and known to follow a normal distribution. Your job is to conduct a hypothesis test to determine if the mean etch rate is different for two different (independent) etching solutions. Assume that the two population variances are unknown but equal. Write out all 7 steps. For Step 5, use α = 0.05. For Step 6, use Minitab for the computations - be sure to check your settings under Options. For Step 7, be sure to include both a statistical conclusion and a practical interpretation. Sample Data : Two random samples of 10 wafers for etch solution have been collected. The observed etch rates are in the table (in mils/min).

3 ENED 3061 Probability & Statistics HW 10: NHST Two Means - p. Spring 2023, Murphy due by 8:00AM on Thursday April 6 1. Parameters of interest ate mean etching rate μ 1 and μ 2 with ∆ 0 = 0 2. H 0 : μ 1 = μ 2 3. H 1 : μ 1 ≠μ 2 4. Test statistic: t because the population variances are unknown but assumed equal (Case 1) t calc = ´ x 1 −´ x 2 − ∆ 0 s p √ 1 n 1 + 1 n 2 and df = n 1 + n 2 − 2 5. Rejection region (two-sided): α = 0.05 and df = n 1 + n 2 − 2 = 10 + 10 − 2 = 18 t 0.025,18 = ± 2.101 t calc < t 0.025,18 Or the p-value is less than α = 0.05 6. Used Minitab t calc = 9.970 − 10.400 − 0 ( 0.340 ) √ 1 10 + 1 10 =− 2.83 p − value = 0.011 7. Conclusion: t calc is less than -2.101 so we reject H 0 and conclude that there is a statistically significant difference in mean etching rate at α = 0.05 Also note that the p-value (0.011) is less than α = 0.05 , which also indicates a statistically significant difference. Practical Conclusion: The mean etching rates are not equal

5 ENED 3061 Probability & Statistics HW 10: NHST Two Means - p. Spring 2023, Murphy due by 8:00AM on Thursday April 6 1. Parameters of interest: The two population variances σ A 2 and σ B 2 in mils min 2. H 0 : σ A 2 = σ B 2 but since we are using F which is a ration, we can also think of it as H 0 : σ A 2 σ B 2 = 1 3. H 0 : σ A 2 σ B 2 ≠ 1 4. Test Statistic: F calc = s 1 2 s 2 2 5. Rejection Region: We will compare the calculated p-value to our alpha of 0.05 6. p − value = 0.087 7. Conclusion: Fail to reject H 0 and conclude that Sample 1 has the same variability as Sample 2 Practical Conclusion: The variances of the two samples are the same