Given X₁, X₂, X3, X4-N(μ, 9) and suppose we have the following hypothesis of interest: Ho:μ = 25 VS H: μ < 25 Jse CR = {XIX ≤ 23) and (0) = P(rei. Ho 10) and determine the significance level and power of a test.
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- 3. Consider a test of H0: u=55 versus Ha: u<55 performed. Make the appropriate conclusion for the given situation: z-value=-1.75, a=.05, p-value=.0401. a. reject H0 b. fail to reject H0 4. Consider a test of H0: u=40 versus Ha: u>40 performed. Make the appropriate conclusion for the given situation: z=-2.5, a=.01, p-value=.0062. a. reject H0 b. fail to reject H0Consider the data. х, | 2 6 13 20 9 17 10 27 24 (a) What is the value of the standard error of the estimate? (Round your answer to three decimal places.) (b) Test for a significant relationship by using the t test. Use a = 0.05. State the null and alternative hypotheses. O Ho: B, + 0 H: B, = 0 O Ho: B, 2 0 H: B, < 0 O Ho: B, = 0 H: B + 0 O Ho: Bo = 0 H: Bo + 0 O Ho: Bo + 0 H: B, = 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject H. We cannot conclude that the relationship between x and y is significant. O Do not reject Hn. We conclude that the relationship between x and y is significant. O Reject H. We conclude that the relationship between x and y is significant. O Do not reject H.. We cannot conclude that the relationship between x and y is significant.The mean height of a certain kind of plant is 173 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 173. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. Ho: 0 H: 0 S OSuppose E(X) = 1.50, E(Y) = 0.55, E(XY) = 0.80, Var(X) = 0.25, and Var(Y) = 0.2475 for two random variables X and Y. Which of the following can be said about the relationship between the X and Y variables? note: no explanantion needed just the answer A:weak positive relationship b:weak negative relationship d:strong negative relationship c:strong positive relationshipThe mean height of a certain kind of plant is 167 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 167. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. H: 0 H;: 0 OIf the results of the test with the following hypotheses are statistically significant, we have found evidence that: Hypotheses: h0: u1 = u2 ha: u1>u2 A: X<x2 B: x1 is not equal to x2 c: u1>u2 D: u1=u2 E: x1>x2 F: u1<u2X .Xs are a random sample from a N(u, 5) population. To test the hypothesis Ho : u = 110 vs H: = 112 a statistician uses the test: Reject H if X > c, where c is a %3D real number. a) Define the terms level of significance and power of a test. b) Find the value of c for which this test will have a significance level of 0.05. (Give your answer to 2 decimal places) Hint: If X,..Xs~ N(.5) then whatis the distribution of X? In particular, what is its distribution under H ? .... c) Determine the power of the test for the value of c found in (b).CBS news reported that 4% of adult Americans have a food allergy consider selecting 10 adult Americans at random define the variable x as: x= number of people in the sample of 10 that have a food allergy a. p(x<3) b. p(x lesss than or equal to 3) c. p (x greater than or equal to 4) d. p (1 less than or equal to x less than or equal to 3)Q1. Let X; and S be the mean and variance of independent random samples of size ni from populations with mean H; and variance of (i = 1,2), respectively where u, = 20. of = 9, n1 = 36 and u2 = 18, ož = 16, n2 = 49. Find (- a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S} > s3) = 0.80 e) P(X1 – X2 > 0.2336) n P(SE/S글 > 0.8368) %3DQ1. Let X and S be the mean and variance of independent random samples of size n; from populations with mean H; and variance of (i = 1, 2), respectively where u, = 20, of = 9, n = 36 and 4z = 18, ož = 16, n2 = 49. Find (using MINITAB or Tables of cdf) a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S{ > s{) = 0.80 e) P(X, - X2 > 0.2336) ) P(S{/S > 0.8368) %3D %3DSuppose a researcher uses 36 pairs of identical twins (i.e., dependent data) to compare two treatments. For each set of twins, one twin is randomly assigned to Treatment 1 and his/her twin is assigned to Treatment 2. In evaluating the calculated t value, how many degrees of freedom (df) does the researcher have?A. 36B. 72C. 35D. 37Researchers were interested in assessing whether stress levels are different at the beginning of the semester compared to finals week. To test this, stress was measured in 5 students at the start of the semester and then again at the end of the semester during finals week. Participant Stress 1 Stress 2 1 22 22 2 32 34 3 24 25 4 28 30 5 26 29 Then H0: μ2 - μ1 ≠ 0, true or false?SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage