Please solve the following questions:-
It has been claimed that no more than 5% of the units coming off an assembly line are defective. Formulate a null hypothesis and an alternative hypothesis for this situation. Will the test be one- tail or two-tail? Why? If the test is one-tail, will it be left-tail or right-tail? Why?If the population standard deviation is known, but the sample size is less than 30, what assumption is necessary to use the z-statistic in carrying out a hypothesis test for the populationFor each of the following tests and z values, determine the p-value for the test: a. Right-tail test and z = 1.54 b. Left-tail test and z = -1.03 C. Two-tail test and z = -1.83For a sample of 35 items from a population for which the standard deviation is o = 20.5, the sample mean is 458.0. At the 0.05 level of significance, test H,: p = 450 versus H, : J = 450. Determine and interpret the p-value for the test.For a sample of 12 items from a normally distributed population for which the standard deviation is 5 17.0, the sample mean is 230.8. At the 0.05 level of significance, test Hip $ 220 versus H, :y > 220. Determine and interpret the p-value for the test.A quality-assurance inspector periodically examines the output of a machine to determine whether it is properly adjusted. When set properly, the machine produces nails having a mean length of 2.000 inches, with a standard deviation of 0.070 inches. For a sample of 35 nails, the mean length is 2.025 inches. Using the 0.01 level of significance, examine the null hypothesis that the machine is adjusted properly. Determine and interpret the p-value for the test.In the past, patrons of a cinema complex have spent an average of $5.00 for popcorn and other snacks, with a standard deviation of $1.80. The amounts of these expenditures have been normally distributed. Following an intensive publicity campaign by a local medical society, the mean expenditure for a sample of 18 patrons is found to be $4.20. In a one-tail test at the 0.05 level of significance, does this recent experience suggest a decline in spending? Determine and interpret the p-value for the test.Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to "drift" away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches. At the 0.01 level of significance, does the machine appear to be in need of maintenance and calibration? Determine and interpret the p-value for the test.A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3 hours, with a standard deviation of 0.20 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 15 novices require a mean of 2 90 hours to complete the job. Assuming the population of times is normally distributed, and using the 0.05 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test.( DATA SET ) Note: Exercises require a computer and statistical software. According to bankrate.com, the average cost to remodel a home office is $10,526. Assuming a population standard deviation of $2000 and the sample of home office conversion prices charged for 40 recent jobs performed by builders in a region of the United States, examine whether the mean price for home office conversions for builders in this region might be different from the average for the nation as a whole. The underlying data are in file XR10033. Identify and interpret the p-value for the test. Using the 0.05 level of significance, what conclusion will be reached?( DATA SET ) Note: Exercises require a computer and statistical software. A machine that fills shipping containers with driveway filler mix is set to deliver a mean fill weight of 70.0 pounds. The standard deviation of fill weights delivered by the machine is known to be 1.0 pounds. For a recent sample of 35 containers, the fill weights are listed in data file XR10034. Using the mean for this sample, and assuming that the population standard deviation has remained unchanged at 1.0 pounds, examine whether the mean fill weight delivered by the machine might now be something other than 70.0 pounds. Identify and interpret the p-value for the test. Using the 0.05 level of significance, what conclusion will be reached?Based on sample data, a confidence interval has been constructed such that we have 90% confidence that the population mean is between 120 and 180. Given this information, provide the conclusion that would be reached for each of the following hypothesis tests at the
