5- Show that 2 (X(-X)² n is a biased estimator of population variance (²)? Show that it is a consistent estimator. Is it as efficient as s²=E=1(X(-X)² n-1
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- Let x1, x2, and x3 be a random sample from and exponential distribution with mean θ. Suppose that θhat = (x1+x2)/2 is an estimator of θ. 1. Find out if the estimator is biased or unbiased. [Show your solution.] 2. Compute for the variance of the given estimator.Show that (X+1)/(n+2) is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased?A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
- 4. If H0 is true, then the proportion of left-handed girls must be the same for the proportion of left-handed boys. Determine Chi square statistics. (write the result .XXXX) 5. If H0 is true, then the proportion of left-handed girls must be the same for the proportion of left-handed boys. Determine Chi square statistics for alpha of .05 (write the result in X.XXX) 6. Conclude and discuss the resultsThe proportion of people in a given community who have Covid-19 infection is 0.005. A test is available to diagnose the disease. If a person has Covid-19, the probability that the test will produce a positive signal is 0.009 . If a person does not have the Covid-19, the probability that the test will produce a positive signal is 0.01. What is the probability that the test will generate positive signal? Which model/rule will best be good for solving the above problem and why? Comment on the types of events you see in the problem and name them.If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?
- In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normaldataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are in fact equal.The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?If x1, x2, . . . , xn are the values of a random sample from a normal population with the known standard deviation σ, find the maximum likelihood estimator for µ (the mean of the population)Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?