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A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting & workers at random and timing each worker on each assembly process. Half of the workers 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 minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 71 56 2 63 3 66 43 68 4 5 6 58 81 15 20 -2 13 71 90 80 41 82 9 7 64 36 16 (a) State the null hypothesis H, and the alternative hypothesis H₁. Ho: O H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: t 5 8 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly time for Process 1 exceeds that of Process 2? Answer this question by performing a hypothesis test regarding (which is with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Hd Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) 0 54 (e) At the 0.05 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2? OYes No 28 H X ㅁ 0=0 D X S P OSO 00 O

A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting & workers at random and timing each worker on each assembly process. Half of the workers 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 minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 71 56 2 63 3 66 43 68 4 5 6 58 81 15 20 -2 13 71 90 80 41 82 9 7 64 36 16 (a) State the null hypothesis H, and the alternative hypothesis H₁. Ho: O H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: t 5 8 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly time for Process 1 exceeds that of Process 2? Answer this question by performing a hypothesis test regarding (which is with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Hd Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) 0 54 (e) At the 0.05 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2? OYes No 28 H X ㅁ 0=0 D X S P OSO 00 O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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圖 A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting & workers at random and timing each worker on each assembly process. Half of the workers 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 minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 71 56 2 63 3 43 68 4 66 71 90 15 20 - 2 5 6 58 81 13 9 80 7 (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: 0 H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: 41 82 64 36 54 16 5 8 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly time for Process 1 exceeds that of Process 2? Answer this question by performing a hypothesis test regarding (which is with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) 0 28 (e) At the 0.05 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2? OYes No H |x X 0=0 O X S OSO 0*0 O<O Р P 010 A S O<O
Transcribed Image Text:圖 A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Process 1 is the standard process used for several years, and Process 2 is an updated process hoped to bring a decrease in assembly time. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting & workers at random and timing each worker on each assembly process. Half of the workers 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 minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 - Process 2) Send data to calculator 1 71 56 2 63 3 43 68 4 66 71 90 15 20 - 2 5 6 58 81 13 9 80 7 (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho: 0 H₁:0 (b) Determine the type of test statistic to use. Type of test statistic: 41 82 64 36 54 16 5 8 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly time for Process 1 exceeds that of Process 2? Answer this question by performing a hypothesis test regarding (which is with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the critical value at the 0.05 level of significance. (Round to three or more decimal places.) 0 28 (e) At the 0.05 level, can the company conclude that the mean assembly time for Process 1 exceeds that of Process 2? OYes No H |x X 0=0 O X S OSO 0*0 O<O Р P 010 A S O<O
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