Two samples were taken from 2 populations. A sample of n=8 from population 1 had a standard deviation of 8.20. The sample of n=5 from population 2 had a standard deviation of 10.44. Perform a hypothesis test to compare if population 1 has a larger variance. Use a significance level of 1%; ?=0.01. State the hypotheses Ho: H1: The test statistic is F= (State accurate to 2dp) The critical value from tables is Fc= F Fc, so Ho The variance of population 1 is population 2
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20^2}{10.44^2} \right) = 0.7662 \] ** Show more…
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In a test of two population means with unknown variances, two independent samples of n1 = 8 and n2 = 10 were taken. The data is given below. Both populations are normally distributed: Sample From Population 1: 12, 10, 20, 20, 11, 13, 8, 9 Sample From Population 2: 20, 19, 16, 23, 17, 17, 18, 17, 10, 18 (a) You wish to test the hypothesis that both populations have the same variance. Choose the correct statistical hypotheses: Ho: σ1 = σ2 Ha: σ1 ≠ σ2 (b) Determine the value of the test statistic for this test. Use at least two decimals in your answer: Test Statistic (c) Determine the P-value for this test, to at least three decimal places. (d) Using a significance level of 0.05, the null hypothesis should be rejected if the variation in Population 1 is statistically different from the variation in Population 2.
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Use Table 5 in Appendix $B$ to find the critical value(s) for the alternative hypothesis, level of significance $\alpha,$ and sample sizes $n_{1}$ and $n_{2}$. Assume that the samples are random and independent, the populations are normally distributed, and that the population variances are (a) equal and (b) not equal. $$H_{a}: \mu_{1} \neq \mu_{2}, \alpha=0.01, n_{1}=19, n_{2}=22$$
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