Determine the rejection region? if H0: σ2=σ2 HA: σ^2 > σ^2 a=0.10, n1 =16 and n2 =11
Determine the rejection region? if H0: σ2=σ2 HA: σ^2 > σ^2 a=0.10, n1 =16 and n2...
Identify the null and alternative hypothesis and find the critical t-value(s), t0, and the rejection region(s) for a t-test to test the claim that μ1 ≠ μ2. Assume that the variance is equal between the populations and use α = 0.10. Assume n1 = 50 and n2 = 45. H0: Ha: T0 = Rejection Region =
Consider the hypothesis test H0: σ1 = σ2 against H1: σ^21 ≠ σ^22 with known variances s1 ^2= 2.3 and s^2 2 = 1.9. Suppose that sample sizes n1 = 15 and n2 = 15. Use α = 0.05. a. Parameter of Interest b. Null and Hypothesis c. test statistic d. reject Ho if e. computation f. conclusion
Independent random samples of n1 = 120 and n2 = 120 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 62 successes, and sample 2 had 67 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions p1 and p2. (a) State the null and alternative hypotheses. - H0: (p1 − p2) = 0 versus Ha: (p1 − p2) ≠ 0 - H0: (p1 − p2)...
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
) observations, where σ
2 > 0 is
unknown. Consider testing
H0 : σ
2 = σ
2
0 versus H1 : σ
2
6= σ
2
0
;
where σ
2
0
is known.
(a) Derive a size α likelihood ratio test of H0 versus H1. Your rejection region should
be written in terms of a sufficient statistic.
(b) When the null...
H0 : µ =21.7 verses HA : µ < 21.7 Rejection Region: t <−t89,0.05 =−1.662 t =−1.798 <−t89,0.05 =−1.662 Reject H0 at α =5%. The data show sufficient evidence that the average number of Type 2 fibers is less than 21.7 what is the p-value?
DISTRIBUTION OF SAMPLE VARIANCE:
Xn ~ N(μ, σ2), where both μ and σ are Problem 4 (25 points). Assume that Xi unknowin 1. Using the exact distribution of the sample variance (Topic 1), find the form of a (1-0) confidence interval for σ2 in terms of quantiles of a chi-square distribution. Note that this interval should not be symmetric about a point estimate of σ2. [10 points] 2. Use the above result to derive a rejection region for a level-o...
n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 9. The test statistic equals a. 100 b. 101.88 c. 101.25 d. 64 10. The p-value is between a. 0.025 and 0.05 b. 0.05 and 0.1 c. 0.1 and 0.2 d. 0.2 and 0.3 11. What is your conclusion? Use α = 0.05. a. fail to reject the null hypothesis b. reject the null hypothesis
QUESTION 1 In one-way ANOVA, suppose that there are three treatments with n1 = 5, n2 = 6, and n3 = 5. What is the rejection region for this test at the 5% level of significance? a)F > 3.81 b)F > 3.63 c)F > 3.24 d)F > 4.08 QUESTION 2 In one-way ANOVA, suppose that there are four treatments with n1 = 5, n2 = 6, n3 = 5, and n4 = 4. What is the rejection region for this...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)
Let X1,...,Xn be a random sample from a Normal N(0, σ²). Consider Ho : σ² = 16 vs. Ha: σ² = 4. a)Use the Neyman Pearson lemma to find the best critical region C*. b)If n = 10 and the size of the test is fixed as α = 0.10, find the critical region and the power when Ho is false.