4. days: a) 116 The following components are put on test and fail at the following times in i) 193 65 185 104 154 146 185 Calculate an estimate of the probability of failure at time t using median ranks.
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- a. Compute the p-value for the test (use R). Round to the nearest 3rd decimal place, 0.xxx. b. Make and justify a statistical decision at the α= 0.15 significance level and state your conclu-sions in context of the problem.At 5% level of significance, test if the Penicillium roqueforticolonies grown on malt extract agar are bigger than when grown on Czapek yeast autolysate agar using the given R-software output: Note: write Ho and Ha both in symbols and in words. Ho: Ha: Test procedure: Decision Rule: Computed test statistic and p-value: Decision: Conclusion:Data: The measurements of their diameters (mm.) are as follows: 38.6 39.0 35.2 34.1 32.9 42.4 37.5 52.6 45.9 60.0 29.1 47.7 61.7 41.7 43.5 50.2Use the standard error to construct a approximate prediction interval for Y using an alpha of 5%. (Round your answer to 2 decimal places x x Fuel Economy of Selected Vehicles (n = 73, k = 4) Obs Vehicle CityMPG Length Width Weight ManTran 1 Acura TL 20 109.3 74.0 3968 0 2 Audi A5 22 108.3 73.0 3583 1 3 BMW 4 Series 428i 22 182.6 71.9 3470 0 4 BMW X1 sDrive28i 23 176.5 70.8 3527 0 5 Buice LaCrosse 18 196.9 73.1 3990 0 6 Buick Enclave 17 201.9 79.0 4724 0 7 Buick Regal 21 190.2 73.1 3692 0 8 Cadillac ATS 22 182.8 71.1 3315 0 9 Cadillac CTS 20 195.5 72.2 3616 0 10 Cadillac Escalade 14 202.5 79.0 5527 0 11 Chevrolet Camaro 1SS 16 190.6 75.5 3719 1 12 Chevrolet Cruze LS 26 181.0 70.7 3097 0 13 Chevrolet Impala LTZ 19 201.3 73.0 3800 0 14 Chevrolet Malibu 2LT 25 191.5 73.0 3532 0 15 Chevrolet Spark LS 31 144.7 61.0 2269 1 16 Chevrolet Suburban LTZ 15 224.0 80.5 5674 0 17 Chrysler 200 Touring LX 20 191.7 72.5…
- The value of Young’s modulus (GPa) was determined forcast plates consisting of certain intermetallic substrates,resulting in the following sample observations (“Strengthand Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U-1Mo Intermetallic,” J. of Materials Engr.and Performance, 1997: 46–50):116.4 115.9 114.6 115.2 115.8a. Calculate x and the deviations from the mean.b. Use the deviations calculated in part (a) to obtain thesample variance and the sample standard deviation.c. Calculate s2 by using the computational formula forthe numerator Sxx.d. Subtract 100 from each observation to obtain a sampleof transformed values. Now calculate the samplevariance of these transformed values, and compare itto s2 for the original data.State the t critical value that would be used for a 99% interval based on a sample size of 37.A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim?
- A round spinner is divided into five sections, where the sections do not have the same size. Using the measure of the interior angles, the probability of the spinner landing on any individual space on a spin is calculated and given in the table. Section 1 2 3 4 5 Probability 0.40 0.20 0.20 0.15 0.05 A statistics student is asked to test the integrity of the spinner using a chi-square goodness-of-fit test. What is the minimum number of times the spinner should be spun to conduct this test? A. 5 B. 25 C. 50 D. 100 E. 500Listed below are the lead concentrations in muμg/g measured in different traditional medicines. Use a 0.010.01 significance level to test the claim that the mean lead concentration for all such medicines is less than 1515 muμg/g. Assume that the lead concentrations in traditional medicines are normally distributed. 1212 22.522.5 88 33 9.59.5 22.522.5 12.512.5 13.513.5 10.510.5 10.510.5 What are the null and alternative hypotheses? A. Upper H 0H0: muμequals=1515 muμg/g Upper H 1H1: muμless than<1515 muμg/g Your answer is correct. B. Upper H 0H0: muμequals=1515 muμg/g Upper H 1H1: muμgreater than>1515 muμg/g C. Upper H 0H0: muμgreater than>1515 muμg/g Upper H 1H1: muμless than<1515 muμg/g D. Upper H 0H0: muμequals=1515 muμg/g Upper H 1H1: muμnot equals≠1515 muμg/g Determine the test statistic. negative 1.33 (Round to two decimal places as needed.)…Out of 188 men over age 65 years, 70 were still working. 87 out of 202 women over the age of 65 yearswere still working. At a 0.08 level of significance, can you claim the proportion of men and women workingover the age of 65 is the same? a.)State the hypotheses and label the claim. b) Is the test left-tailed, right-tailed, or two-tailed (circle one)?c) What is/are the critical value(s)? Draw a picture. d) What is the P-value and test-statistic?e) Give two reasons for your decision to reject/not reject H0 based on: 1) Test statistic compared to criticalvalue 2) P-value compared to α Then, state the conclusion by relating back to the original claim.
- With a = .01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ?Use Gaussian quadrature with two-sampling points to determine the values of the following three integrals:The following table shows the number of shirts by sizes that are manufactured in a factory on aparticular week:Extra Small Small Medium Large Extra Large 390 470 520 680 440 c) A machine packages shirt in bags with a mean weight of 3 kg. A random sample of 20 bagshas a mean weight of 3.05 kg with a standard deviation of 0.05kg, From the data given, state thevalue of a:(i) parameter (ii) statistic