Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent,...

Suppose you want 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 σ 2 1 = σ 2 2. At a level of significance of α = 0.05, when should you reject H0?
n1 = 14 n2 = 12 x1 = 21 x2 = 22 s1 = 2.5 s2 = 2.8

Solutions

Expert Solution

Hypothesis: (Claim) Vs

Now use the t-test.

The test is two-tailed test

The pooled estimate is ,

df=degrees of freedom =n1+n2-2=14+12-2=24

The test statistic is ,

The critical values are ,

; From t-table

Decision : Here , the value of the test statistic does not lies in the rejection region

Therefore , fail to reject Ho.

Conclusion : Hence , there is sufficient evidence to support the claim.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose you want to test the claim that μ1 > μ2. Two samples are random, independent,...

Suppose you want 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 ≠ . At a level of significance of , when should you reject H0? n1 = 18 n2 = 13 1 = 595 2 = 580 s1 = 40 s2 = 25

Suppose you want to test the claim that μ1 = μ2. Two samples are random, independent,...

Suppose you want 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 variances of two populations are not the same (σ21≠ σ22). At a level of significance of α = 0.01, when should you reject H0? n1 = 25 n2 = 30 x1 = 27 x2 = 25 s1 = 1.5 s2 = 1.9 Reject H0 if the standardized test...

Test the claim that μ1 = μ2. Two samples are random, independent, and come from populations...

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 σ 21 ≠ σ 22. Use α = 0.05. n1 = 25 n2 = 30 x1 = 18 x2 = 16 s1 = 1.5 s2 = 1.9

Find the critical value, t0, to test the claim that μ1 < μ2. Two samples are...

Find the critical value, t0, to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ21(variance 1)= σ22(variance 2). Use α = 0.05. n1 = 15 n2 = 15 x1 = 22.97 x2 = 25.52 s1 = 2.9 s2 = 2.8

Find the critical values, t0, to test the claim that μ1 = μ2. Two samples are...

Find the critical values, t0, to test the claim that μ1 = μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that . n1 = 25 n2 = 30 1 = 25 2 = 23 s1 = 1.5 s2 = 1.9

Test the claim about the difference between two population means μ1 and μ2 at the level...

Test the claim about the difference between two population means μ1 and μ2 at the level of significance alpha α. Assume the samples are random and independent, and the populations are normally distributed. Claim: 1μ1=2μ2 alphaα=0.01 Population statistics 1σ1=3.33.3, 2σ2=1.61.6 Sample statistics:x overbar 1x1=14, n1=29, 2x2=16, n2=28 Determine the standardized test statistic. Determine P value

1. For a two-tailed, independent samples t-test, the alternative hypothesis would look like μ1−μ2≠0, whereas the...

1. For a two-tailed, independent samples t-test, the alternative hypothesis would look like μ1−μ2≠0, whereas the null hypothesis would look like μ1−μ2=0. True or False? 2. When the null hypothesis is true, the mean of the sampling distribution of differences between means is equal to the mean of the population that the samples represent. True or False? 3. In a related-samples t-test, if there is no treatment effect we expect that μD will equal 0 (zero). True or False?

Consider the hypothesis test with null hypothesis μ1=μ2 and alternative hypothesis μ1 > μ2.Suppose that sample...

Consider the hypothesis test with null hypothesis μ1=μ2 and alternative hypothesis μ1 > μ2.Suppose that sample sizes n1 = 10 and n2 =10, that the sample means are 4.9 and 2.8 respectively, and that the sample variances are 2 and 3 respectively. Assume that the population variances are equal and that the data are drawn from normal distributions. a) Test the hypothesis that at α= 0.05 and provide a conclusion statement b) Provide an adequate confidence interval with 95% confidence...

In Exercises a-c, test the claim about the difference between two population means μ1 and μ2...

In Exercises a-c, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed. a. Claim: μ1 = μ2; α = 0.05. Assume Sample statistics: , X1=228, s1 = 27, n1 = 20 and X2=207, s2 = 25, n2 = 13 b.Claim: μ1 ≤ μ2; α = 0.10. Assume Sample statistics: , X1=664.5, s1 = 2.4, n1 = 40...

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2...

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=24n1=24 with a mean of M1=85.8M1=85.8 and a standard deviation of SD1=19.3SD1=19.3 from the first population. You obtain a sample of size n2=17n2=17 with...

Subjects