A random sample of size n = 70 from a normal population with μ = 0 is to be used to testHo: o² = 2.5 against H₁ : σ² = 3.(a) Use the Neyman-Pearson Lemma to construct the most powerful critical region for a =0.01. Round the critical value to three decimal places.(b) Compute the power of the test. Round your final answer to five decimal places.

(a) Using the Neyman-Pearson Lemma, we know that the most powerful test will reject the null…

Answered: A random sample of size n = 70 from 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

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Let μ denote the true average reaction time to a certain stimulus. For a z test of Ho: μ = 5 versus H₂: μ> 5, determine the P-value for each of the following values of the z test statistic. (Round your answers to four decimal places.) (a) 1.49 (b) 0.99 (c) 1.96 (d) 2.41 (e) -0.15 USE SALT
12c: One researcher estimated that smoking reduces the sense of smell. The mean of the odor test for non-smokers is μ=18.4. The following scores were obtained by giving the same odor test to an unbiased sample of a cigarette smokers: 16 14 19 17 16 17 15 18 19 12 14 18 c) What is the critical t value for alpha=.05?
To test Hoμ= 60 versus H₁ μ<60, a random sample of size n=23 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. Click here to view the t-Distribution Area in Right Tail (a) If x= 57.9 and s= 10.2, compute the test statistic. to=987 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.05 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given. Critical Value: (Round to three decimal places. Use a comma to separate answers 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?
Suppose that we are testing H0: µ = µ0 versus H1: µ > µ0. Calculate the P -value for the following observed values of the test statistic (round all answers to 4 decimal places. (a)z0 = 2.45, (b)z0 = -1.53, (c)z0 = 2.15, (d)z0 = 1.95, (e)z0 = -0.25.
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?
Suppose you are testing H0:μ=96 against Ha:μ< 96. From an SRS of 82 individuals, you compute xˉ= 104 and s= 6.4. What is the value of the t-test statistic in this test? Round your answer to three decimal places. suppose you are testing H0:μ=108 against Ha:μ< 108. From an SRS of 68 individuals, you compute xˉ= 110 and s= 6.4. What are the degrees of freedom for the distribution of test statistic tt?
In a test of HO: μ-25 against HA: μ # 25, a sample of size 125 produces Z = 1.28 for the value of the test statistic. What is the p-value equal to? Use four decimal places. Do not show any work.
A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of 7 cars was selected and were driven for two weeks without the booster and two weeks with the booster. Test Ho:Ho =0 against H1:Hp<0 at a = .05. The critical value for this test is: O 1.943 -2.447 -2.635 -1.943
Let μ denote the true average reaction time to a certain stimulus. For a z test of Ho: μ = 5 versus H₂:μ> 5, determine the P-value for each of the following values of the z test statistic. (Round your answers to four decimal places.) (a) 1.44 (b) 0.95 (c) 1.96 (d) 2.48 (e) -0.11 USE SALT
Consider Ho: H=75 versus H1: µ<75. A random sample of 16 observations taken from this population produced a sample mean of 73.2. The population is normally distributed with o=6 a) Calculate the test statistic (round to two decimal places) b) Use z-table or technology to get the p-value (round to four decimal places)
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. . TInterval (13.046,22.15) x=17.598 Sx=16.01712719 n=50 a. What is the number of degrees of freedom that should be used for finding the critical value tα/2? df=__ (Type a whole number.) b. Find the critical value tα/2corresponding to a 95% confidence level. tα/2= (Round to two decimal places as needed.) c. Give a brief general description of the number of degrees of freedom. A. The number of degrees of freedom for a collection of sample data is the number of unique, non-repeated sample values. B. The number of degrees of freedom for a collection of sample data is the number of sample values that are determined after certain restrictions have been imposed on all data values. C. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary…

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