a) Suppose that Y₁, Y2Y₁ is a random sample from a normal distribution with parameter mean0 and variance e, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level ofsignificance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1.i) Show that the uniformly most powerful test of their hypothesis rejects Ho ify ≥c, where c is a constant that solves the probability equation0.05 = PY² ≥c|0 = 1).ii) What will be the value of c in part a) if n = 15.

Answered: Image /qna-images/answer/16feedca-6d63-46f3-8a2f-8b04b0dd7f8c.jpg

Answered: a) Suppose that Y₁, Y2,..., Y₁ is a…

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

4) We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. Our sampling has 8 African zebras and 6 Arabian horses. We find 3.01 as the absolute value of our standardized test statistic for our sample data. Is this data significant at the .02 level of significance? NONE OF THE OTHERS NO YES
b) Suppose that Y₁, Y₂,..., Y₁0 is a random sample from a bernoulli (P) distribution. It is desired that the null hypothesis Ho: P = 0.5 against the alternative hypothesis H₁: P = 0.1 at a level of significance. If Ho is rejected when Σı Y = 1. i) Determine the level of significance. ii) Find the power of the test.
a) QUESTION 3 Suppose that Y₁, Y2, ..., Yn is a random sample from a normal distribution with parameter mean 0 and variance 0, say N(0,0). If Mr Masela and Mr Sepuru desire to use 5% level of significance to test the null hypothesis Ho: 0 = 1 against alternative hypothesis H₁:0 > 1. i) Show that the uniformly most powerful test of their hypothesis rejects Ho if Σ₁ yc, where c is a constant that solves the probability equation 0.05 = P₁Y≥ c|0 = 1). ii) What will be the value of c in part a) if n = 15.
Please show solutions manually
2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a = 0.01.
i need help finding the pooled variance , estimated standard error, and the t statistics
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.
A psychologist has developed a standardized test for measuring vocabulary skill for 4 year old children. The scores on the test form a normal distribution with u = 70 and o = 20. A researcher would like to use the test to investigate the hypothesis that children who grow up as an only child develop vocabulary skills at a faster rate than children in larger families. A sample of n=25 only children is obtained and the mean test score for the sample is M = 77. Perform a two tailed hypothesis test, with an alpha level of .05, and add an APA summary.
A research tea believes that the weight of Grizzly adule male bears are normally distributed. A simple random saple of 23 Grizzly male bears yielded a mean weight of 277kg and a variance of 121. Let μ denote the mean weight for Grizzly adult male bears. Suppose the research teams wants to test, at the 5 % level of significance, whether the mean weight for Grizzly adult male bears is greater than 271kg. Suppose the assumptions to this hypothesis test are satisifed. a) What are the null and alternative hypothesis, and level of significance, for this hypothesis test? b) What is the distribution of the test statistic for this hypothesis test? c)What is the decision rule for this hypthesis test?
A company that manufactures aerospace parts is considering the possibility of investing in CMU (Cellular Manufacturing Unit). Top Management desires a good estimates distribution characteristic for the FW. There are three random variables i.e., they have uncertainties in their values. An economic analyst is hired to estimate the desired parameters and FW. He concludes that the scenario presented to him is suitable for Monto Carlo simulation because there are uncertainties in three variables and the direct analytical approach is impossible. The company has done a preliminary economic analysis of the situation and provided the analyst with the following estimates: Capital Investment Normally distributed with mean of $150,000 and standard deviation of $12,000 Useful Life Uniformly distributed with a minimum of 5 years and maximum 10 years Market value $25,000 (single outcome) Annual net cash flow $15,000 probability 0.9 $20,000 probability 0.5 $25,000 probability…
A two-sample study for the difference between two population means will utilize t-test procedures and is to be done at the 0.05 level of significance. The sample sizes are 23 and 27. The variances are 18 and 36, respectively. What is the upper critical value t, for the rejection region if:(a) the alternative hypothesis is one-sided, and you assume that the population variances are vunequal?(b) the alternative hypothesis is two-sided , and you assume that the population variances are unequal?(c) the alternative hypothesis is one-sided and you assume that the population variances are equal?(d) the alternative hypothesis is two-sided, and you assume that the population variances are equal?
A researcher would like to conduct a hypothesis test to determine if the mean age of faculty cars is less than the mean age of student cars. A random sample of 25 student cars had a sample mean age of 7 years with a sample variance of 20, and a random sample of 32 faculty cars had a sample mean age of 5.8 years with a sample variances of 16. What is the critical value of the rejection region if the difference is taken as student - faculty and the test is conducted using a 5% significance level?

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