Question 3 (2.5 points) Saved A factory is considering replacing some older machines. They decided that if the proportion of defective items the machine produces is significantly more than 3% it will be replaced. A sample of 500 items produced on an older machine showed that 19 of them are defective. At a significance level of 10% does the factory get rid of the machine? Ho: 0.03 HA: 0.03 z-stat (Round to 2 decimal places) = 1.0486 p-value (Do not round) = 0.1472 What is your decision (Retain Ho or Reject Ho)? Reject Ho Question 4 (0.25 points) Saved Which statement correctly summarizes the outcome of the hypothesis test. The sample data suggests that the proportion of defective items the machine produces is not significantly more than 3%. The sample data suggests that the proportion of defective items the machine produces is significantly more than 3%. The sample data suggests that the proportion of defective items the machine produces is significantly less than 3%. The sample data suggest that the proportion of defective items is significantly more than 3.8% Question 5 (1 point) BONUS: What number (or proportion) of defective items would they have needed to see in order to Reject Ho?
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Eleven percent of the products produced by an industrial process over the past several months have failed to conform to specifications. The company modifies the process in an attempt to reduce the rate of nonconformities. In a random sample of 300 items from a trial run, the modified process produces 30 nonconforming items. Do these results provide evidence that the modification is effective in reducing the rate of nonconformities? You may assume conditions for inference are satisfied. Answer in the blanks to show the work associated with exploring this claim. To explore the suspicion above, conduct a significance test using the hypotheses: p = 0.11 p ___________ 0.11 Blank #1: Determine the correct alternative hypothesis by filling in the blank with <, > or not equals. Blank #2: Report the test statistic to two decimal places Blank #3: Report the p-value to four decimal places Blank #4: Give the test decision: (reject or do not reject) H0 Blank #5: Evidence ______________(favors or does not favor) that the modified process has reduced the rate of nonconformities Blank #6: How large a sample, n, would you need to estimate p with margin of error 0.03 with 95% confidence (use z = 1.96)? Use p* = 0.10, the sample proportion given in the problem. Use rounding rules for sample size determinations in reporting your answer. Blank #7: After computing the sample size above with your initial desired confidence level and margin of error, you've decided realistically that you cannot afford the determined n. To decrease the calculated n, you could (increase or decrease) the margin of error?
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Two machines are used to fill 50 lb bags of litter. A sample of 50 bags is selected from machine 1 (sample 1) and weighed. The average weight of the bags of litter from this sample was 49 pounds with a standard deviation of 12. A sample of 54 bags is selected from machine 2 and weighed. The average weight of the bags of litter from this sample was 52 pounds with a standard deviation of 11 pounds. Conduct a hypothesis test at a 0.05 significance level to test if the average weight of the bags of litter is significantly different between the two machines. The alternative hypothesis is (enter choice 1, 2, or 3). 1. μ1 > μ2 2. μ1 < μ2 3. μ1 ≠ μ2 What is the estimate of (μ1 - μ2)? The value of the test statistic z = (round denominator to the 100th place and round the final answer to the 100th place). Conclusion: Do not reject the null hypothesis. There is not enough evidence to claim that μ is significantly different than μ. There is not sufficient sample evidence to claim that the average weight of 50-pound bags of litter is significantly different between the two filling machines.
A certain bag of fertilizer advertises that it contains 7.25 kg, but the amounts these bags actually contain is normally distributed with a mean of 7.4 kg and a standard deviation of 0.15 kg. The company installed new filling machines, and they wanted to perform a test to see if the mean amount in these bags had changed. Their hypotheses were H0: μ = 7.4 kg vs. Ha: μ ≠ 7.4 kg (where μ is the true mean weight of these bags filled by the new machines). They took a random sample of 50 bags and observed a sample mean of 7.36 kg and a standard deviation of 0.12 kg. They calculated that these results had a p-value of approximately 0.02. 1) What conclusion should be made using a significance level of α = 0.05? A. Fail to reject H0 B. Reject H0 and accept Ha C. Accept H0 2) In context, what does this conclusion say? I. The evidence suggests that these bags are being filled with a mean amount that is different than 7.4 kg. II. We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4 kg. III. The evidence suggests that these bags are being filled with a mean amount of 7.4 kg. 3) How would the conclusion have changed if they had instead used a significance level of α = 0.01? i. They would have rejected Ha. ii. They would have accepted H0. iii. They would have failed to reject H0. iv. They would have reached the same conclusion using either α = 0.05 or α = 0.01.
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