Suppose X₁,..., Xn when n > 2 are i.i.d Bernoulli(p) where 0 < p < 1 is unknown.(a) Find a sufficient statistic T(X₁,..., Xn) for p.(b) Show that 1 {X₁ = 1, X₂ = 0} is an unbiased estimator of p(1-p), where 1 {} denotesthe indicator function.(c) Use the Rao-Blackwell theorem to improve the above estimator.

It is given that X1, X2, ........, Xn follows Bernoulii distribution with parameter = p.

Answered: (a) Find a sufficient statistic…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

One consumer wants to know if the average number of chips is less than 45 in a bag of Red Bird potato chips. A random sample of 100 was selected and the sample statistics werex=41.6 and s = 7.6. (i) What is the standard error of x? (ii) Using one or two sentences, briefly describe the Central Limit Theorem (CLT) for the sample mean. (ii) Does CLT hold for this test? Explain your reasoning. (iv) State the hypotheses for the test. (v) Give a 90% CI (3 d.p.) for the average amount of chips in each bag (The margin of error is 1.262). (vi) Interpret your Cl in part (iv) in context. (vii) Make a decision and conclusion based on your Cl in part (v).
Is it possible to have more than one unbiased estimator for an unknown parameter? Or is not possible? How so?
For the situation described below, state the null and alternative hypotheses to be tested. (Enter != for ≠ as needed.) A new variety of pearl millet is expected to provide an increased yield over the variety presently in use, which has a mean yield of about 55 bushels per acre.
4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?
The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…
(5) If Xis a r.v. with mean u and variance o?, using Chebyshev's-Inequality, AX-2 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.
A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set u = P(Y = 1) and the following model is fit: logit(u) = Bo + BịI(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Bo -4.565 0.128 0.380 0.087 B2 Вз -0.198 0.042 0.163 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence…
Albumin is a liver protein that helps circulate vitamins throughout the body. Reduced Albumin has been associated with severe illness with Covid-19 patients. Suppose we wanted to conduct a study to compare the mean Albumin concentration (g/L) between a sample of adult patients hospitalized for Covid 19 (Sample Mean= 32.8, s=6.0) to the mean albumin concentration (g/L) of healthy adults (u=34.1, o=7.13). How many patients would need to enroll from the hospital to conduct this study with 99% confidence, and 80% power? A. 267 B. 120 C. 352 D. 225
Regarding the picture, I just need help finding the F ( , ) F(,)=, R-squared, Adj R-squared And I need help testing the null hypothesis.
Plz answer correctly asap
1. In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (d) Conclusion of the test above is Reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure.
1. You are interested in the effect of a new learning technique. The performance score on the test before applying the new learning technique is 50 (u=50), the standard deviation is 4 (o=4). You obtained a sample of 64 subjects and applied the new learning technique. After that, their performance score on the test increased by 2 (x=52). Did the new learning technique improve/had any effect on the performance? The answer, using 4 steps of hypothesis testing. Please use APA style to report your result. Assume that a-level=.05 2. You are interested in the effect of a new learning technique. The performance score on the test before applying the new learning technique is 50 (u=50), the standard deviation is 24 (o=24). You obtained a sample of 64 subjects and applied the new learning technique. After that, their performance score on the test increased by 2 (x=52). Did the new learning technique improve/had any effect on the performance? The answer, using 4 steps of hypothesis testing.…

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

(a) Find a sufficient statistic T(X₁,..., Xn) for p. (b) Show that 1 {X₁ = 1, X₂ = 0} is an unbiased estimator of p(1-p), where 1 {} denotes the indicator function. (c) Use the Rao-Blackwell theorem to improve the above estimator.