The last 15 months of sales data are givenbelow:JanFebMar AprMay202013.714.714.8 1314202116.9 16.3 14.7Xt represents sales in month t. Let Yt = log (xt)and let Zt = Yt - Yt-12. Then the following modelwas fitted:Zt = 0.52Zt-1 +0.38Zt-2 + Et where Et is whitenoise.c. Compute the forecasts for Xt for April 2021and May 2021.Jun Jul13.4 13.6Aug14.9Sep13.5Oct Nov Dec14.715.721.9

The value of variable Yt for each value corresponding to Xt is as follows Month Xt Yt Jan-20…

Answered: The last 15 months of sales data are…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Since the Cobot’s gripper is a critical component, a reliability of 99% is desired for that component. The failure time, in hours, of the cobot’s gripper follows a lognormal distribution with µt=10.52 and σt= 1.44. the gripper is considered a consumable item (i.e., if failed, the gripper is replaced, not repaired. a. What is the MTTF? b. At what number of hours of use should the gripper be replaced to meet the desired 99% reliability?
A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and σ = 0.5. Let X be the strength of a randomly sampled specimen of this composite. a) If the claim is true, what is P(X < 20)? b) Based on the answer to part (a), if the claim is true, would a strength of 20 MPa be unusually small? c) If you observed a tensile strength of 20 MPa, would this be convincing evidence that the claim is false? Explain. d) If the claim is true, what is P(X < 130)? e) Based on the answer to part (d), if the claim is true, would a strength of 130 MPa be unusually small? f) If you observed a tensile strength of 130 MPa, would this be convincing evidence that the claim is false? Explain.
An assemb ly-line worker at Joseph Milner'sFabrication Shop inserts Pa rt A into Part B. A time study wasconducted and produced the fo llowing results in seconds: 8.4, 8.6,8.3, 8.5, 8.7, 8.5. What is the average cycle time?
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?
Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid (in dpm, disintegrations per minute) was then determined for each culture, yielding the following observations. 7,255 6,875 9,637 6,863 9,098 5,846 8,954 7,979 7,068 7,498 7,882 8,179 7,528 8,728 7,469 Suppose that it is known that the mean rate of uptake for cultures without nitrates is 8,000. Do the data suggest that the addition of nitrates results in a decrease in the mean rate of uptake? Test the appropriate hypotheses using a significance level of 0.10. Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t= P-value= State your conclusion. Reject H0. We have convincing evidence that the mean rate of…
The article “Effect of Internal Gas Pressure on the Com- pression Strength of Beverage Cans and Plastic Bottles” (J. of Testing and Evaluation, 1993: 129–131) includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. What assumptions are necessary for your analysis? ( use ? = 0.01 )
The Federal Aviation Administration requires material used to make evacuation systems retain their strength over the life of the aircraft. In an accelerated life test, the principal material, polymer-coated nylon weave, is aged by exposing it to 158 degrees F for 168 hours. The tensile strength of the specimens of this material is measured beforea nd after the aging process. The following data (in psi) are recorded: Specimen Original Aged 1 215 203 2 226 216 3 226 217 4 219 211 5 222 215 6 231 218 7 234 224 8 219 210 9 209 201 10 216 207 Is there evidence to support the claim that the nylon weave tensile strength is the same before and after the aging process? Use the P-value approach.
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).a) Find the probability that the demand will exceed 200 cfs during the early afternoon on arandomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will exceed capacity on a randomly selected day isonly .01?
A theoretical justification based on a certain material failure mechanism underlies the assumption that ductile strength X of a material has a lognormal distribution. Suppose the parameters are μ = 4.8 and σ = 0.11. What is the value of median ductile strength? (Round your answer to three decimal places.) If ten different samples of an alloy steel of this type were subjected to a strength test, how many would you expect to have strength of at least 125? If the smallest 5% of strength values were unacceptable, what would the minimum acceptable strength be?
Determine the probability of failure of a steel tension member in a truss that supports widely varying snow loads given the following data on the loading placed on the member (Q) and the member strength (R); Q = 8,000 lbs and COV = 0.27 and R = 15,000 lbs and COV = 0.08. First solve assuming that each variable, Q and R were represented by a normal distribution and then resolve assuming that each was best represented by a log-normal distribution.
Find the root mean square of y=1/x in the interval [1,3]. Round to the nearest hundredth.RMS =

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