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# Problem II. (22 points) A group of students in STAT 3021 want to test whether the...

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Problem II. (22 points) A group of students in STAT 3021 want to test whether the state- ment "The breaking strength of Brand A cotton threads is larger than the Brand B" is true. These students randomly selected 10 Brand A cotton threads and 10 Brand B cotton threads. Assume that population distributions for both Brands A and B are approximately independent normal. The breaking strength of each brand is indicated in following table. The data and relevant R commands and outputs are given below. Answer the following questions from 1 though 5. Brand A 208.5, 187.6, 194.6, 205.8, 188.8, 209.1, 207.2, 208.8, 181.5, 200.5 Brand B 198.8, 212.2, 177.3, 155.1, 219.3, 191.4, 201.4, 188.1, 191.7, 156.0 > B1<-c(208.5, 187.6, 194.6, 205.8, 188.8, 209.1, 207.2, 208.8, 181.5, 200.5) > B2<-c(198.8, 212.2, 177.3, 155.1, 219.3, 191.4, 201.4, 188.1, 191.7, 156.0) > mean (B1) [1] 199.24 > mean (B2) [1] 189.13 > sd(B1) [1] 10.34442 > sd (B2) [1] 21.33052
1. (4 points) State the null and alternative hypothesis that test whether the breaking strength of Brand A cotton threads is larger than the Brand B. Use the correct statistical notations and define the parameters of interest. 2. (4 points) From Chapter 10, we learned that there are three different test statistics we use to conduct an independent two-sample test; (i) z-test statistic, (ii) t-test statistic with pooled estimate, and (iii) t-test statistic with non-pooled estimate. Which test statistic is the most appropriate in this problem? Explain why. (No need to calculate the value of test statistic) 3. (4 points) It is known that p-value is 0.1002. Draw the conclusion in context of the problem. Use the significant level a = 0.05.
4. (5 points) State (i) type 1 error and (ii) type 2 error in this problem. (iii) Which error could you have made based on your answer from the previous question? 5. (5 points) Suppose the sample size for each group was 50. (50 Brand A cotton threads, 50 Brand A cotton threads). If we still have the same sample means and the same sample standard deviations for both groups, dose it change your conclusion from Problem 3? Calculate the new p-value and support your answer.

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