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This file contains independent observations on a random variable X. It is known that a2-1.4246. a...
The following observations are from two independent random samples, drawn from normally distribut...
The following observations are from two independent random samples, drawn from normally distributed populations. Sample 1 9.74, 9.04, 8.06, 6.09, 7.51 Sample 2 |[25.96, 26,27, 26,34, 39.09, 33.88, 28.87, 33.46] We are interested in testing the null hypothesis that the two population variances are equal, against the one-sided alternative that the variance of Population 1 is larger than the variance of Population 2. Define Population 1 to be the population with the larger sample variance a) What are the appropriate...
The observations from a random sample of n = 6 from a normal population are: 13.15,...
The observations from a random sample of n = 6 from a normal population are: 13.15, 13.72, 12.58, 13.77, 13.01, 13.06. Test the null hypothesis of H0:μ=13 against the alternative hypothesis of H1:μ<13. Use a 5% level of significance. Answer the following, rounding off your answer to three decimal places. (a) What is the sample mean? (b) What is the sample standard deviation? (c) What is the test statistic used in the decision rule? (d) Can the null hypothesis be...
6. Suppose that you observe three independent Poisson observations Y1: Y, Y3 with means λ,A2,A3 respectively....
6. Suppose that you observe three independent Poisson observations Y1: Y, Y3 with means λ,A2,A3 respectively. We to test Ho:A-A2 (a) Show that the chi-squared test statistic for testing this nul hypothesis is b) Suppose we looked at this a different way. Ignore Ys and treat this as a binomial experi ment where n = Yİ + ½. Then test the null hypothesis Ho : p = 1 /2 versus the two sided alternative. Using a normal approximation for large...
Suppose there is a random sample of 400 observations, divided into four groups. The table below...
Suppose there is a random sample of 400 observations, divided into four groups. The table below summarizes the count of observations that were seen in each group. Group 1 160 Group 2 120 Group 3 40 Group 4 80 = P2 = pz = PA = 0.25, against the alternative hypothesis We are interested in testing the null hypothesis Ho: P HA: At least one proportion is incorrect a) What is the expected count for each of the groups? Expected:...
We are looking to calculate the power of a one-sided test from n independent observations xi...
We are looking to calculate the power of a one-sided test from n independent observations xi from a N (µ, σ2 ) distribution with a null hypothesis of H0 : µ = µ0 and an alternative H1 : µ > µ0. Supposing that we know σ2, we can form a test statistic T = (x¯ − µ0)/(σ/√n) and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power...
We are looking to calculate the power of a one-sided test from n independent observations from...
We are looking to calculate the power of a one-sided test from n independent observations from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μο and an alternative H1 : μ > μο. Supposing that we know σ2, we can form a test statistic o/Vn and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power of this test against the alternative that μ-A-This power...
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations....
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations. Sample 1 F1 = 23.65 = 2.50 p1 = 18 Sample 2 F2 = 25.62 = 3.28 p2 = 20 Test the null hypothesis Ho: P1 = r2 against the alternative hypothesis HA : H1 CH2 a) Calculate the test statistic for the Welch Approximate procedure. Round your response to at least 3 decimal places. Number b) The Welch-Satterthwaite approximation to the degrees of...
The data in this file are the differences in productivity of workers measured before and after...
The data in this file are the differences in productivity of workers measured before and after they undertake a training program. Compute the p-value for the null hypothesis that the training program makes no difference to productivity. Using a significance level of 5% and a two-sided alternative hypothesis, do you reject H0? Do you need to make any assumptions in order for your test to be valid? In your answer, you should state the null and alternative hypotheses, the significance...
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations....
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations. Sample 1 F1 = 22.49 11 = 2.54 P1 = 15 Sample 2 F2 = 27.31 3 = 3.08 P2 = 18 Test the null hypothesis HO : H1 = 2 against the alternative hypothesis HA: MI <H2 a) To save you on calculations, I will tell you that the standard error of the difference in sample means (SE(X_1 bar - X_2 bar)) is...
Independent random samples of n = 150 and n = 150 observations were randomly selected from...
Independent random samples of n = 150 and n = 150 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 68 successes, and sample 2 had 74 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions P, and py: (a) State the null and alternative hypotheses. O Ho: (P1 - P2) = 0 versus Ha: (P1-P2) < 0 O Ho: (2,-) < versus H: (2,-2)...
The following observations are from two independent random samples, drawn from normally distributed populations. Sample 1 9.74, 9.04, 8.06, 6.09, 7.51 Sample 2 |[25.96, 26,27, 26,34, 39.09, 33.88, 28.87, 33.46] We are interested in testing the null hypothesis that the two population variances are equal, against the one-sided alternative that the variance of Population 1 is larger than the variance of Population 2. Define Population 1 to be the population with the larger sample variance a) What are the appropriate...
6. Suppose that you observe three independent Poisson observations Y1: Y, Y3 with means λ,A2,A3 respectively. We to test Ho:A-A2 (a) Show that the chi-squared test statistic for testing this nul hypothesis is b) Suppose we looked at this a different way. Ignore Ys and treat this as a binomial experi ment where n = Yİ + ½. Then test the null hypothesis Ho : p = 1 /2 versus the two sided alternative. Using a normal approximation for large...
Suppose there is a random sample of 400 observations, divided into four groups. The table below summarizes the count of observations that were seen in each group. Group 1 160 Group 2 120 Group 3 40 Group 4 80 = P2 = pz = PA = 0.25, against the alternative hypothesis We are interested in testing the null hypothesis Ho: P HA: At least one proportion is incorrect a) What is the expected count for each of the groups? Expected:...
We are looking to calculate the power of a one-sided test from n independent observations from a N(μ, σ2) distribution with a null hypothesis of Ho : μ-μο and an alternative H1 : μ > μο. Supposing that we know σ2, we can form a test statistic o/Vn and reject the null hypothesis when T > 1.645. This test has level α = 0.05. We want a formula for the power of this test against the alternative that μ-A-This power...
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations. Sample 1 F1 = 23.65 = 2.50 p1 = 18 Sample 2 F2 = 25.62 = 3.28 p2 = 20 Test the null hypothesis Ho: P1 = r2 against the alternative hypothesis HA : H1 CH2 a) Calculate the test statistic for the Welch Approximate procedure. Round your response to at least 3 decimal places. Number b) The Welch-Satterthwaite approximation to the degrees of...
Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations. Sample 1 F1 = 22.49 11 = 2.54 P1 = 15 Sample 2 F2 = 27.31 3 = 3.08 P2 = 18 Test the null hypothesis HO : H1 = 2 against the alternative hypothesis HA: MI <H2 a) To save you on calculations, I will tell you that the standard error of the difference in sample means (SE(X_1 bar - X_2 bar)) is...
Independent random samples of n = 150 and n = 150 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 68 successes, and sample 2 had 74 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions P, and py: (a) State the null and alternative hypotheses. O Ho: (P1 - P2) = 0 versus Ha: (P1-P2) < 0 O Ho: (2,-) < versus H: (2,-2)...
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