b. Alpha is 10%, the sample size is 45 and sigma is known.
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- Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)16 Find the significance level of a two tailed test if the critical value of t is 1.746 and the sample size is 17. Answer:If you let X1, X2, X3, X4 equal the cholesterol level of a woman under the age of 50, a man under 50, a woman 50 or older, and a man 50 or older, respectively. Assuming the distribution of Xi is N(μi, σ2), i = 1, 2, 3, 4 and you test the null hypothesis H0: μ1 = μ2 = μ3 = μ4, using seven observations of each Xi, what would be the critical region for an alpha = 0.05 significance level?
- Find the critical value of t a/2 that corresponds to a degree of confidence of 90% and a sample size of 8.A certain statistic will be used as an unbiased estimator of a parameter. Let R represent the sampling distribution of the estimator for samples of size 35, and let S represent the sampling distribution of the estimator for samples of size 15. Which of the following must be true about R and S ? (A) The expected values of R and S will be equal, and the variability of R will be less than the variability of S. (B) The expected values of R and S will be equal, and the variability of R will be equal to the variability of S. (C) The expected values of R and S will be equal, and the variability of R will be greater than the variability of S. (D) The expected value of R will be greater than the expected value of S, and the variability of R will be greater than the variability of S. (E) The expected value of R will be greater than the expected value of S, and the variability of R will be less than the variability of S.A random sample of n= 4 individuals is selected from a population with μ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05.
- Find the t values that form the boundary of the critical region in the right-hand tail for a one tailed test with α=.01 for each of the following sample sizes: A) n=10 B) n=20 c) n=30#1. Find the t values that form the boundary of the critical region for a two-tailed significance test at the α = .01 significance level for a sample size n = 20. #2. A random sample of n = 4 individuals is selected from a population with μ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. Using a two-tailed test at the α = .05 significance level, does the treatment have a significant effect? a. State the null and research hypotheses b. State the critical t-values c. Calculate t for the sample mean d. Evaluate the null hypothesis e. Calculate Cohen’s D and describe the effect size10. If the critical value of "t" is 1.699, and significance level "a" is 5% .Find the sample size.
- A certain statistic will be used as an unbiased estimator of a parameter. Let R represent the sampling distribution of the estimator for samples of size 35, and let S represent the sampling distribution of the estimator for samples of size 15. Which of the following must be true about R and S? The expected values of R & S will be equal, and the variability of R will be less than the variability of S. The expected values of R and S will be equal, and the variability of R will be equal to the variability of S The expected values of R and S will be equal, and the variability of R will be greater than the variability of S The expected value of R will be greater than the expected value of S , and the variability of R will be greater than the variability of S The expected value of R will be greater than the expected value of S, and the variability of R will be less than the variability of S.. Find the critical values (“z”, "? ? "?? “t” scores) for the following. a. C.L. = 98%, n is 25 and σ is unknown. b. Alpha is 3%, the sample size is 45 and sigma is known. d. α is .5%, n=15;sigma is known for the left tail (not “z”) e. 90%, chi-square right, when the sample size is 22.( ? ? ?)A random sample of n=4 individuals is selected from population with µ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M= 40. 1 with SS= 48. a. How much difference is there between the mean for the treated sample and the mean for the original population?(note: In a hypothesis test, this value forms the numerator of the t statistic.) b. If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard the standard error for M. (note: in a hypothesis test, this value is the denominator of the t statistic.) c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α=.05.