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- A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 995 590 510 539 739 917 571 555 916 728 664 693 708 887 849 At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.A recent poll found that 664 out of 1026 randomly selected people in a particular country felt that colleges and universities with big sports programs placed too much emphasis on athletics over academics. Assuming the conditions for the CLT are met, use the accompanying Minitab output to complete parts a and b below. N Event Sample p 95% CI for p 1026 664 0.647173 (0.617934, 0.676413) Question content area bottom b. Suppose a sports blogger wrote an article claiming that a majority of adults from this country believe that colleges and universities with big sports programs place too much emphasis on athletics over academics. Does this confidence interval support the blogger's claim? Explain your reasoning. A. No, it is not a plausible claim because the confidence interval contains 50%. B. No, it is not a plausible claim because the confidence interval does not contain only values above 50%. C. Yes, it is a…The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose (for now) that one-third of all American households own a pet cat. Is this number (one-third) a parameter or a statistic? Explain. What symbol is used to represent the number? What does the Central Limit Theorem say about how the sample proportion of households who own a pet cat could vary under repeated random sampling? Comment on shape, center, and spread of the distribution. Also draw a well-labeled sketch of this sampling distribution. Still supposing that one-third of all American households own a pet cat, between what two values do you expect 95% of all sample proportions to fall? Explain why the interval in part (3) turns out to be so narrow. This survey found that 31.6% of the households sampled owned a pet cat. Is this number a parameter or a statistic? Explain. What symbol is used to represent the value? Indicate this…
- A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms. Full data set Carpeted Uncarpeted 10.9 9.6 7.1 9.9 11 8.8 15.7 10 14.5 11.1 8.2 8.7 10.9 15.5 7.6 7.5 Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. A. H0: μ1<μ2 H1: μ1>μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1=μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1≠μ2 Determine the P-value for this hypothesis test. P-value=nothing (Round to three decimal places as needed.) State the…A manufacturer of flashlight batteries claims that the average life of her batteries is larger than 400 hours. Peter, as a quality assurance officer in the manufacturing company, took a random sample of 13 batteries from a day’s production and used them continuously until they failed to work. The lifetime (hours) until failure was:342 426 317 545 264 451 1049 631 512 266 492 562 298 (a) At the 0.05 level of significance, is there evidence that the manufacturer’s claim is correct? (b) What is the p-value?An online retailer claims that 90% of all orders are shipped within 12 hours ofbeing received. A consumer group placed 121 orders of different sizes and atdifferent times of days; 102 orders were shipped within 12 hours.a. Compute the sample proportion of items shipped within 12 hours.b. Confirm that the sample is large enough to assume that the sample proportionis normally distributed. Use p = 0.90, corresponding to the assumption that theretailer’s claim is valid.
- Ms. Tina is the accountant in the Walton Industries. She believes that the current cash-flowproblem at Walton is due to the slow collection of accounts receivable. She believes that morethan 60 percent of the accounts are in arrears more than three months. A random sample of200 accounts showed that 140 were more than three months old. At the 0.05 significancelevel, can she conclude that more than 60 percent of the accounts are in arrears for more thanthree months?The data processing department of the Arizona Bank has five data entry clerks. Each working day their supervisor verifies the accuracy of a random sample of 250 records. A record containing one or more errors is considered defective and must be redone. The results of the last 30 samples are shown in the table. All were checked to make sure that none was out of control. Sample Number of DefectiveRecords Sample Number of DefectiveRecords Sample Number of DefectiveRecords Sample Number of DefectiveRecords 1 2 3 4 5 6 7 8 7 5 19 10 11 8 12 9 9 10 11 12 13 14 15 16 6 13 18 5 16 4 11 8 17 18 19 20 21 22 23 12 4 6 11 17 12 6 24 25 26 27 28 29 30 Total 7 13 10 14 6 11 9 300 a. Based on these historical data, set up a p-chart using z = 3.b. Samples for the next 4 days showed the following: Sample Number of Defective Records Tues Wed Thurs Fri 17 15 22 21 What is the supervisor’s assessment of the data-entry process likely to be?Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. 0.1860.2050.2550.3050.1910.2120.2660.2980.1880.2220.2780.3070.1970.2460.2900.311 Yes. The correlation between the expected z-scores and the observed data, nothing, exceeds the critical value, nothing. Therefore, it is reasonable to conclude that the data come from a normal population. B. Yes. The correlation between the expected z-scores and the observed data, nothing, exceeds the critical value, nothing. Therefore, it is not reasonable to conclude that the data come from a normal population. C. No. The correlation between the expected z-scores and the observed data, nothing, does not exceed the critical value, nothing. Therefore, it is reasonable to conclude that the data come from a normal population. D. No. The…
- A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 PM lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. Another bank in the area is also concerned with the noon-to-1 PM lunch period. A random sample of 12 customers is selected from each bank and the waiting times are the following: Bank 1: 4.02 4.13 4.05 4.09 3.2 3.79 4.95 4.74 4.29 4.7 3.8 3.18 Bank 2: 2.28 3.85 1.61 3.25 2.82 2.61 3.93 2.13 3.03 1.89 3.7 2.45 Is there evidence of a difference in the variability of the waiting time between the two branches? (alpha = 0.05) a. What are the null and alternate hypotheses? H0: H1:…A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 PM lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. Another bank in the area is also concerned with the noon-to-1 PM lunch period. A random sample of 12 customers is selected from each bank and the waiting times are the following: Bank 1: 4.02 4.13 4.05 4.09 3.2 3.79 4.95 4.74 4.29 4.7 3.8 3.18 Bank 2: 2.28 3.85 1.61 3.25 2.82 2.61 3.93 2.13 3.03 1.89 3.7 2.45 Is there evidence of a difference in the variability of the waiting time between the two branches? (alpha = 0.05) c. Compute the value of the test statistic? (Round your answer to 2 decimal places. Negative values should have a minus sign in front of them) d.…a Light bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 10 of its light bulbs resulted in the following lives in hours. 993 595 512 839 739 917 871 755 918 729. At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the P value method of testing hypothesis