School of Mathematics and StatisticsTe Kura M¯atai TataurangaSTAT292Update 3Week 3Assignment 2Assignment 2 is due onTuesday, 24 March 2020 at 11:59 PM. Note that lateassignments are not accepted and will not be marked (i.e., will receive a mark of 0) unlessillness, bereavement, or other substantial causes occur and have been discussed with thecourse coordinator.1
STAT292Tutorial 2Week 31. Which of the following could be a Poisson random variable?
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2. The number of red mites found on 98 randomly selected leaves is as shown below:Number of red mites (r)Frequency (fr)020135223315445061a.Is the probability distribution of the number of red mites consistent with aPoisson distribution? Be sure to carry out the following steps:i. State the hypotheses to be tested.ii.Calculate expected frequencies, and determine an appropriate grouping ofthe unique counts for numbers of mites on a leaf.iii.Calculate the test statistic, and write down the distribution of the teststatistic under the null hypothesis.iv.Determine thep-value of the test, and make your conclusion at theα= 0.1significance level.b.Repeat the steps carried out in part (a), but now test whether the probabilitydistribution is Poisson with meanλ= 1.7. (Think carefully about how thehypotheses will change and how this will impact the expected frequencies.)Carry out this test at theα= 0.05significance level.3.Consider a random sample ofn= 437students from the approximately 30,000students enrolled in a large public university.The following table classifies thestudents by their field of study and whether or not the student has a loan.No Student LoanStudent LoanAgriculture3532Engineering13798Management5124Science29312