A factory manufacturing light-emitting diode (LED) bulb claims that their light bulbs last for 90,000 hours on average. To confirm if this claim was valid, a quality control manager got a sample of 300 LED bulbs and obtained a mean lifespan of 85,000 hours and the standard deviation of the manufacturing process is 45000 hours. Use the 90% confidence level.
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- According to some studies, a vacuum cleaner uses an average of 46 kilowatt hours per year. If a sample of 12 homes shows that vacuum cleaners use an average of 42 kilowatt hours per year with a standard deviation of 11.9 kilowatt hours, does this suggest at the 0.05 level of significance that vacuum cleaners use, on average, less than 46 kilowatt hours annually? Conduct an appropriate test to answer this.Assume the population of kilowatt hours to be normal.A major car manufacturer wants to test a new engine to determine whether it meets air pollution standards. The mean emission levels of all engines must be not more than 60 parts per million (ppm) of carbon. 10 engines are manufactured for test and the sample mean and standard deviation are 61.1 ppm and 3.0 ppm respectively. Do these data provide sufficient evidence to conclude that this engine does not meet the pollution standards? Using 5% level of significance.The sample mean weight of 200 adult vulturine parrots was measured to be 734.2 grams, with a standard deviation of 15.7 grams. Using a 10% level of significance, what could we claim about the population mean weight for all vulturine parrots so that the hypothesis will fail to be rejected?
- The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 21 tires surveyed, the mean lifespan was 46500 miles. Using alpha = 0.05, can we prove that the data is inconsistent with the manufacturers claim? We should use a test. What are the correct hypotheses? H0: Ha: Based on the hypotheses, find the following: Test Statistic= p-value=A state fish hatchery raises trout for stocking streams and lakes. The size of the fish at release time canbe controlled to a fair degree by varying the rate of feeding. The target is a mean of 14 ounces; if the fishare too small, those who catch the fish aren’t happy. A random sample of 82 fish were weighed at time ofrelease and it was determined that the mean was 13.78 ounces with a standard deviation of 1.84 ounces.Test to determine if the fish being released have a population mean less than 14 ounces at the 0.05significance level.A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 30 tires surveyed, the mean lifespan was 45,900 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim? A-State the distribution to use for the test. (Round your answers to two decimal places.) B-What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) C-What is the p-value? (Round your answer to four decimal places.) D-Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) E-
- The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1800 pounds and a standard deviation of 95 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1800 pounds. To see if this is the case, 70 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1829 pounds. Can we support, at the 0.10 level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1800 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the value of the test statistic. Round to three or more decimal…Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An article reported on a pilot study in which each of 55 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 192 and the sample standard deviation was 89. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content? Test the appropriate hypotheses at significance level 0.001. State the appropriate null and alternative hypotheses. Ο H: μ - 153 H: u > 153 Ο H: μ= 153 H: u = 153 Ο H μ= 153 Ha: u < 153 Ο H: μ= 153 H,: us 153 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = p-value = State the conclusion in the problem context. O Reject the null hypothesis. There is sufficient evidence…A manufacturing company wants to create a warranty for their product, but wants to ensure that they do not have to replace more than 12% of their products. They found that the lifetime of the product is normally distributed with a mean of 3.8 years and a standard deviation of 5 months. What should they use for a warranty?
- The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 28 tires surveyed, the mean lifespan was 46500 miles. Using alpha = 0.05, can we prove that the data in inconsistent with the manufacturers claim? We should use a test. What are the correct hypotheses? H0: Ha: Based on the hypotheses, find the following:Test Statistic=p-value= The correct decision is to . The correct conclusion would be:The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 60 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1775 pounds. To see if this is the case, 90 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1788 pounds. Can we support, at the 0.05level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. a. State the null hypothesis H0 and the alternative hyposthesis H1. b. Find the value of the test statistic. c. Find the p-value. d. Can we…The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 21 tires surveyed, the mean lifespan was 41500 miles. Using alpha = 0.05, can we prove that the data in inconsistent with the manufacturers claim? What is the Test Statistic