### Comparing Assembly Times for Keyboard Manufacturing ProcessesA company is investigating whether there is a difference in assembly times between two keyboard assembly processes. Since assembly times can vary significantly from one worker to another, the company selects 12 workers at random to control this variability. For each worker, assembly times are recorded for both processes. The table below shows these times in minutes:| Worker | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 ||--------------|----|----|----|----|----|----|----|----|----|----|----|----|| Process 1 | 90 | 41 | 42 | 78 | 45 | 39 | 32 | 91 | 30 | 75 | 45 | 81 || Process 2 | 78 | 22 | 32 | 38 | 52 | 43 | 35 | 30 | 40 | 65 | 49 | 50 || Difference (Process 1 - Process 2) | 12 | 19 | 10 | 40 | -7 | -4 | -3 | 61 | -10 | 10 | -4 | 31 |### Hypothesis TestingUsing these data, the company wants to determine if there is a statistically significant difference in assembly times between the two processes. They will do this at the 0.05 level of significance.#### Steps:1. **Formulate Hypotheses:** - Null Hypothesis \( H_0 \): The mean difference in assembly times between the two processes is zero (\(\mu_d = 0\)). - Alternative Hypothesis \( H_1 \): The mean difference in assembly times between the two processes is not zero (\(\mu_d \neq 0\)).2. **Perform a Two-tailed Test:** - Assume the population of differences is normally distributed. - Calculate necessary statistics and test the hypothesis.3. **Conclude:** - Interpret the results based on the p-value or critical value approach.Given these methods and data, the company will be able to ascertain whether the two processes significantly differ in terms of assembly time. ### Hypothesis Testing ExerciseThis exercise guides you through the steps of hypothesis testing using a specified significance level. Below are the steps involved:#### (a) State the Hypotheses- **Null Hypothesis (H₀):** - Input box for defining the null hypothesis.- **Alternative Hypothesis (H₁):** - Input box for defining the alternative hypothesis.#### (b) Determine the Type of Test Statistic- **Type of Test Statistic:** - Dropdown menu for selecting the appropriate test statistic to use.#### (c) Find the Test Statistic- Calculate the value of the test statistic and round it to three or more decimal places. - Input box for entering the calculated value.#### (d) Find Critical Values- Determine the two critical values at a 0.05 level of significance, rounded to three or more decimal places. - Input boxes for entering the two critical values.#### (e) Conclusion at 0.05 Level- Question: At the 0.05 level, can the company conclude that the mean assembly times for the two processes differ? - Options: Yes / No (radio buttons)### Symbols and Tools- The right panel includes various symbols and tools useful for input such as: - Greek letters (e.g., μ, σ) - Mathematical operators (e.g., ≤, ≠) - Statistical symbols (e.g., x̄, s)This exercise helps in understanding the practical application of hypothesis testing by identifying null and alternative hypotheses, selecting the correct test statistic, calculating the test statistic value, finding critical values, and making conclusions based on statistical evidence.© 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use

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worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. rkers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in min corded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 90 Explanation 78 Check 12 2 41 22 19 3 N 40 32 8 4 65 38 5 65 52 (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₁ :0 H₁ :0 Start 2 6 35 7 7 8 32 38 39 23 9 76 10 43 38 33 11 55 27 13 28 -7 15 38 10 -4 59 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer question by performing a hypothesis test regarding H (which is u with a letter "d" subscript), the population mean difference in assembly times for t processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answ specified. (If necessary, consult a list of formulas.) 12 LL 81 X 50 31 O S 2022 McGraw Hill LLC. All Rights Reserved. P ê Terms of Use | Priva

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P