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- A Texas Garden Center wants to store leftover packets of vegetable seeds from their spring sale to have for their fall sale, but the center is concerned that the seeds may not germinate at the same rate six months later. The manager randomly selects a packet of green bean seeds remaining from the spring sale and plants them as a test. Although the packet claims a germination rate of 92% of the seeds, only 171 of the 200 test seeds sprout. Is this evidence that the seeds have lost viability during their six months in storage?7. The manufacturer of an Engine Energizer System (EES) claims that it improves gas mileage and reduces emissions in automobiles by using magnetic-free energy to increase the amount of oxygen in the fuel for greater combustion efficiency. Following are test results, performed under international and U.S. government agency standards, on a random sample of 14 vehicles. The data (also see file M09_Gas_Paired.txt or M09_Gas_Q7.xlsx) give the carbon monoxide (CO) levels, in parts per million, of each vehicle tested, both before installation of EES and after installation. (a)Test at the 1% significance level whether, on average, EES reduces CO emissions (b)Obtain a 99% confidence interval for the difference between the mean CO emissions before and after installation of EES corresponding to the test in part (a) (c)Interpret the confidence interval obtained in part (b). Does this interval support the conclusion of the hypothesis test in part (a)? Justify your answerData collected over a number of years show that whena broker called a random sample of eight of her clients,she got a busy signal 6.5, 10.6, 8.1, 4.1, 9.3, 11.5, 7.3, and5.7 percent of the time. Assuming that these figures canbe looked upon as a random sample from a continuous uniform population, use the estimators obtained in Exer-cise 57 to estimate the parameters α and β.
- A humane society claims that less than 39% of U.S. households own a dog. In a random sample of 402 U.S. households, 155say they own a dog. At α=0.01, is there enough evidence to support the society's claim? (a) Write the claim mathematically and identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.A problem with a telephone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telephone company. The Sheet 8 contains samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines: test the Null hypothesis that the time to clear the problem doesn't significantly differ across to centers at the 0.03 level. Sheet 8 Location 1. Location 2 1,48 7,55 1,75 3,75 0,78 12,00 2,85 1,10 0,52 0,60 1,60 0,52 4,15 3,30 3,97 2,10 1,48 0,58 3,10 13,00 1,02 3,75 0,53 0,65 0,93 1,92 1,60 0,60 0,80 1,53 1,05 4,23 6,32…Calculateaconfidenceinterval for the me-dian ofthe second population.Select your confidenc eleve land reportit with your answer.??
- If X is a random variable having the standard normaldistribution and Y = X2, show that cov(X, Y) = 0 eventhough X and Y are evidently not independent.A student attempted to use L’Hopital’s Rule as follows. Did the student make an error, if any, or does it state “no error”?The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modifica-tion in the chemical composition of her paint, the manu-facturer wants to test the null hypothesis μ = 20 minutes against a suitable alternative, where μ is the average dry-ing time of the modified paint. (a) What alternative hypothesis should the manufactureruse if she does not want to make the modification in thechemical composition of the paint unless it decreases thedrying time?(b) What alternative hypothesis should the manufactureruse if the new process is actually cheaper and she wants tomake the modification unless it increases the drying timeof the paint?
- Suppose that the makers of Duracell batteries want to demonstrate that their size AAbattery lasts an average of at least 45 minutes longer than Duracell’s main competitor,the Energizer. Two independent random samples of 100 batteries of each kind areselected, and the batteries are run continuously until they are no longer operational. Thesample average life for Duracell is found to be 308 minutes. The result for the Energizerbatteries is 254 minutes. Assume the entire AA batteries standard deviation 84 minutesand Duracell batteries 67 minutes. Is there evidence to substantiate Duracell’s claim thatits batteries last, on average, at least 45 minutes longer than Energizer batteries of thesame size? (assuming equal population variances)A tax accountant would like to test the claim that the proportion of individuals who owe when filing their taxes is less than 0.20. If the z− test statistic was calculated as z=−2.11, does the tax accountant have enough evidence to reject the null hypothesis? Assume α=0.005. Move the blue dot to choose the appropriate test (left-, right, or two-tailed). Then, use the graph below to show the test statistic, p-value, and the rejection region to make a conclusion about the hypothesis test. powered by Move the blue dot to choose the appropriate test α=0.01 α=0.025 α=0.05 α=0.1 Significance level = 0.01 Select the correct answer below: There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is not enough evidence to suggest the proportion of individuals who owe when filing their taxes is less than 0.20. There is enough evidence to suggest the proportion of individuals who owe when filing their taxes is greater than 0.20.…1) A cement producer, manufactures and then fills 40kg-bags of powder cement on twodistinct production tracks located in separate suburbs. To determine whether differencesexist between the average fill rates for the two tracks, a random sample of 25 bags fromTrack 1 and a random sample of 16 bags from Track 2 were recently selected. Each bag’sweight was measured and the following information measures from the samples arereported:Production ProductionTrack 1 Track 2n1 = 25 n2 = 16x2 = 40.02 x1 = 39.87 s1 = 0.59 s2 = 0.88 Supervision believes that the fill rates of the two tracks are normally distributed with equalvariances.Construct a 95% confidence interval estimate of the true mean difference between the twotracks.--------------------------------------------------------------------------------------------------------------2) Two independent simple random samples were selected from two normallydistributed populations with unequal variances yielded the following information:Sample 1…
