2) If X1, X2, ..., X, is a random sample from a distribution having p.d.f ofthe formf(r; 0) = 0xº-1, 0

The Neymann-Perason Lemma will be used to find the best critical regiol for given hypotheses.

Answered: show that a best critical region for…

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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A test of H0: µ ≥ 59 versus H1: µ < 59 is performed using α = 0.05. The value of the test statistic z = -1.80. If the true value of µ is 59, does the conclusion you reach result in Type I error, Type II error, or the correct decision? a. Type I Error b. Type II Error c. correct decision d. not enough information
You are using a z-test to test H0: u=400 vs Ha: u<400 at the a=.05 level. What would the rejection region be for this test?
Using the chart below, Given 6 degrees of freedom and an ?=0.05, what is the critical value of X2 for 1-(?/2)?
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 54 women over the age of 50 used the new cream for 6 months. Of those 54 women, 43 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 60% of women over the age of 50? Test using α=0.05. test statistics z= The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that p=0.6. That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 60% of women over 50.B. We can reject the null hypothesis that p=0.6 and accept that p>0.6. That is, the cream can improve the skin of more than 60% of women over 50.
Let s be the sample variance of a random sample of size n1 fron a Normal(41,o²) population and s, be the sample variance of a random sample of size 12 from a Nornal(µ2,0²) population and the two samples are independent. Note that the two samples have the same population variance o² but µi # j12 and n1 # 12. Define the pooled variance estimator as (n1 – 1)sỉ + (n12 – 1)s3 T1 + n2 - 2 -- Is s? unbiased for o2 ? Explain with precisc computation. Find the distribution of ºP. Give the reasoning of your answer. Find the variance of s.
Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.33 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.39 parts per million and the standard deviation is 2.09 parts per million. At a = 0.05, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. (a) Identify the claim and state H, and Ha. Which of the following correctly states H, and H,? Ho: = |2.33 Hạ: < 2.33 (Type integers or decimals. Do not round.) The claim is the alternative hypothesis. (b) Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are to = (Use a comma to separate answers as needed. Round to two decimal places as needed.)
The t statistic for a test of Ho u 15 H₁ μ<15 based on n = 10 observations has the value t = -1.61. (a) What are the degrees of freedom for this statistic?
A group of 15 first graders were asked to complete a manual dexterity test. Six students completed it in more than 7 minutes while eight students completed it in less than 7 minutes. At α = 0.05, test the claim that the median time for all first graders is 7 minutes. A. What is the test statistic? B. What is the critical value?
Is there a difference among the 3 treatments in the table below? Test using α = .05 Treatment A Treatment B Treatment C 2 3 2 ∑X2 = 280 2 3 4 G = 60 3 4 5 N = 15 3 5 6 k = 3 5 5 8 SS1 = 6 SS2 = 4 SS3 = 20 What is the value of the critical F boundary? (from the tables)
18% of all college students volunteer their time. Is the percentage of college students who are volunteers smaller for students receiving financial aid? Of the 392 randomly selected students who receive financial aid, 55 of them volunteered their time. What can be concluded at the αα = 0.01 level of significance? H0: H1: The test statistic ? t z = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is ? > ≤ α
A group of 15 first graders were asked to complete a manual dexterity test. Six students completed it in more than 7 minutes while eight students completed it in less than 7 minutes. At αα = 0.05, test the claim that the median time for all first graders is 7 minutes. A. What is the test statistic? B. What is the critical value?

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show that a best critical region for testing H : 0 = 1 vs Ha : 0 = 2 is C = ((11, x2, ..., n) : c < II1 Ti).