could you please do a to c B2. Consider the testing problem where we have observed a random sample x₁, ...,Xn fromthe model X₁,..., Xn ~ N(µ, 0²), where the X, are independent, and we want to testthe hypothesis Ho: o² = o against the alternative H₁: 0² ‡ 0². For the test we usethe test statisticy =ni=1-2(x₂ − x)²0²/where is the sample mean of the xi.(a) What are the type I errors and type II errors in this testing problem?(b) If Ho is true, what is the distribution of the random variable Y corresponding to y?(c) Assume that n = 20 and we reject Ho if and only if y > 32.852. What is theprobability of a type I error in this case?(d) Assume now that H₁ is true for the test in part (c). Draw a sketch of the type IIerror as a function of o2. (There is no need to calculate explicit values.)(e) Explain why the test described in part (c) is not a good test for testing the hypoth-esis Ho: 0² o against the alternative H₁: 0² # of. How would you improvethe test?

In this problem we are performing hyposthesis testing on distribution for testing For the test we…

Answered: Xn from Consider the testing problem…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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According to a researcher, the average level of mercury uptake in wading birds in Everglades has declined over the past several years. Ten years ago, the average level was 15 parts per million (ppm). Suppose we are interested in testing whether the average level today is less than 15 ppm. Describe the type I error for the test of hypothesis. O The mean mercury level is equal to 15 ppm when in fact the mean is less than 15 ppm. O The mean mercury level is less than 15 ppm when in fact the mean is equal to 15 ppm. O The mean mercury level is greater than 15 ppm when in fact the mean is equal to 15 ppm.
T= DF=
Please help me for Question 4
3 For an SRS {4₁};=, from the normal distribution. ==// (Y-M) 2 fy (y;u, 0²) - 1 е värvoze Show that the sample mean I is a consistent estimator,
Use the following data to answer question 8 - 12. A number of studies have claimed evidence that the first-born in a family is, on the whole, more likely to be "successful" than later-borns. A study along this direction compared the IQs of a random sample of 80 first-borns with those of an independent random sample of 105 later-borns. The data are summarized below: Sample size Sample mean Sample SD First-borns 80 112 7.2 Later-borns 105 108 8.0
3 For an SRS {Y: 3;=, from the normal distribution fy (y;u, 0²) = ==// (Y-M) ² 2, ▷ √rvoze Show that the sample mean I is a sufficient estimator,
Suppose that X1,..., X, is a random sample from a normal distribution with mean u and variance o?. Two unbiased estimators of o? are ởf = s° = E(x, - Xy°, and ô = (X1 - 2 Find the efficiency of ở relative to ôž.
you are testing ho: u=0 against ha=u not equal 0 based on an SRS of four observations from a normal population. what are the values of the t static are statistically signification at a=0.005 levels? (a) t>7.453 (b) t<-7.453 or t>7.453 (c) t<-5.598 or t >5.598
random sample of size 36 from a population with known variance = 9 yields a sample mean of 17. The Z value that corresponds to α = 0.05 that is used to test H0: μ=μ0 versus Ha: μ>μ0 is (The answer must be rounded to three decimal places.)
Suppose that a sample of T=36 recent college graduates is used estimate the model y, = B+e, where y, is the hourly wage rate. We have: y = $22.2,o² = 36 (a) Test whether the mean wage for recent college graduates is $20/hour at a = 1% (Be sure to state the null and the alternative hypotheses, the test statistics, their distribution and d.f., and your decision for this test). (b) Construct a 90% confidence interval estimation for B.
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The average yield of soybeans in Ohio is 58 bu/Acre (the control mean). We wish to test whether a field that has been treated with the product has soybean yields that are different than 58 bu/acre. We are going to conduct a study with 49 fields and set up the hypothesis at α=.05. After we conduct the experiment we get a sample mean x = 60 bu/Acre and s=7 bu/acre. Conduct the test. Z=____________

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