The test statistic for Ho: σ12=σ22 is Fo = S21/S22 where the S2iare the sample variances of two random samples from independent normal populations. true or false
The test statistic for Ho: σ12=σ22 is Fo = S21/S22 where the S2iare the sample variances...
Problem 3. Consider two independent samples, X1, . . . , Xm from a N(µ1, σ12 ) distribution and Y1, . . . , Yn from a N(µ2, σ22 ) distribution. Here µ1, µ2, σ12 and σ2 are unknown. Consider testing the null hypothesis that the two population variance are equal, H0 : σ12 = σ22 , against the alternative that these variances are different, H1 : σ12 ≠ σ12 . (a) Derive the LR test statistic Λ
In a two-tailed F-test about equality of two population variances, given n1=21, S21 = 8.2, n2=26,S22= 4.0, and alpha = 0.05. The numerator and denominator degrees of freedom for the F distribution, respectively, are: The computed value of the test statistic, F, is: The critical value of F, from F chart or using MS Excel, is: The p-value, from F chart or using MS Excel, is: The conclusion is to reject H0. True or False?
A random sample of leading companies in South Korea gave the following percentage yields based on assets. 2.1 2.3 4.2 1.9 0.5 3.6 2.4 0.2 1.7 1.8 1.4 5.4 1.1 Use a calculator to verify that s2 ≈ 2.125 for these South Korean companies. Another random sample of leading companies in Sweden gave the following percentage yields based on assets. 2.2 3.8 3.9 1.1 3.9 2.8 2.3 3.5 2.8 Use a calculator to verify that s2 ≈ 0.909 for these...
Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows. 6.33 5.84 5.98 5.77 7.31 7.18 7.06 5.79 6.24 5.91 6.14 Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.340. Another random sample of years for a second plot gave the following annual wheat production (in pounds). 5.91 5.77 6.47 6.75...
Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows. 6.96 7.10 5.84 5.91 7.31 7.18 7.06 5.79 6.24 5.91 6.14 Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.384. Another random sample of years for a second plot gave the following annual wheat production (in pounds). 5.91 5.91 5.91 5.91...
The test statistic used in the F test for the equality of two variances is calculated as F = s12/s22. In this formula, s12and s22 represent the sample variance for sample 1 and sample 2, respectively. True or False?
Given the following information: n1=31 , s21=0.489, n2=7, s22=1.797, Ha: σ21≠σ22, α=0.05 Step 1 of 2 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer(s) to four decimal places. step 2 of 2: Make a decision. A. reject null hypothesis B. Fail to reject null hypothesis
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks was fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...
Find the standardized test statistic, t, to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that two populations' variance is the same (σ21= σ22). n1 = 15 n2 = 15 x1 = 25.76 x2 = 28.31 s1 = 2.9 s2 = 2.8
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...