Question 1: (Rice 9.11) Power curves for two-sided z-testSuppose that X₁,..., X, form a random sample from a normal distribution having a knownvariance of 2.(a) Give a formula for the power of the likelihood ratio test of Ho: = 0 versus HA: 0for significance level a as a function of u. (Your function should have a and n asparameters.(b) Plot the graphs of the power versus μ for o² = 100 and n = 25 for significance levels0.10 and 0.05. Do the same for a sample size of n = 100 (there should be four powercurves in total). You can plot them all on a single set axes. Be sure to appropriatelylabel the axes and give a legend. Compare the graphs and explain what you see.

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Answered: 1 (a) Give a formula for the power of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a trivariate distribution 01 = 2, 02 = 03 = 3 12 = 0-7, r23 = r31 = 0-5 %3| Find (1) b12.3 and (i) b13-2.
Construct a 90% confidence interval for u, -la with the sample statistics for mean chalesterol content of a hamburger from two fast food chains and confidence interval construction formula below Assume the populations are approximately normal with unequal variances Stats X =71 mg. s, = 3.99 mg. n = 15 X2 = 59 mg. s2= 2.16 mg na Confidence interval when variances are not equal df is the smaller of n1 or n, - 1 Enter the andpoints of the intanial I Round to the nearest intoger as needed )
Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = x₁ - x₂. Test Ho: M = 0 vs Ha: Ma < O using the paired data in the following table: test statistic = Treatment 1 p-value= Treatment 2 15 12 18 20 Give the conclusion using a 5 % significance level. y.com/was/ui/v2/assessment-player/inday h 14 25 21 15 21 20 11 14 14 Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. 22 15 20
Under the logic of the hypothesis test of ANOVA, the F-statistic is made up of the ratio of Mean Squares between over Mean Squares within: F = MS Between MSwithin If the variance observed in an ANOVA relationship does not have enough of an MS Between effect There is too much noise in your system, and you should try your experiment again to confirm the findings. The F-ratio will approach 1 in the long run, since there is no MS Between effect. The F-ratio will become relatively large, since there is more variance to work with. O The F-ratio will approach 0 in the long run, since the MS Within will cancel out the effect.
a. What are the sample estimates of β0,β1,and β2? b. What is the least squares prediction equation? c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem. d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01. e. Use a 95% confidence interval to estimate β2. f. Find R2 and R^2_a and interpret these values. g. Find the test statistic for testing H0: β1=β2=0. h. Find the observed significance level of the test in part g.interpret the result.
Construct a 90% confidence interval for u, - , with the sample statistics for mean calorie content of two bakeries specialty pies and confidence interval construction formula below Assume the populations are approximately normal with equal variances Bakery A Bakery B X1 = 1823 cal X, = 1629 cal S1 = 155 cal S2 = 190 cal n1 = 10 n2 = 12 Confidence interval when variances are equal n n. (n. - 1) s (n2 - 1) s where G and d.f = n, +n2 - 2 nn, - 2 Enter the endpoints of the interval (Round to the nearest integer as needed.)
Heart rates are determined before and 30 minutes after a Kettleball workout. It can be assumed that heart rates (bpm) are normally distributed. Use the data provided below to test to determine if average heart rates prior to the workout are significantly lower than 30 minutes after a Kettleball workout at the 0.02 level of significance. Let μ₁ = mean before workout. Select the correct Hypotheses: Ho:με 2 με Η: μι = με Η: μη μ₂ O O O Conclusion: before 69 69 65 62 63 61 after 73 75 72 70 68 59 O Fail to Reject Ho ● Reject Ho Test Statistic = p-value = Ho:μd = 0 H₁: Hd ‡0 O [three decimal accuracy] [three decimal accuracy] Ho:μα 20 Ha:Pa 0 O Interpret the conclusion in context: ● There is enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout. O There is not enough evidence to suggest the mean bpm before a Kettleball workout is lower than 30 minutes after the workout.
Use the t-distribution and the sample results to complete the test of the hypotheses. Use a 5 % significance level. Assume the results come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal. Test Ho : µ = 10 vs Ha : µ > 10using the sample resultsI = 13.2, s = 8.7, with n = 12. (a) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = p-value =
A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. Use μ1 for the mean number of families with no children. At α=0.10, is there a difference between the means? Use the P-value method and tables. (a) State the hypothesis and identify the claim with the correct hypothesis. H0: ▼(Choose one) H1: ▼(Choose one) This hypothesis test is a ▼(Choose one) test. (b)Find the critical value(s). Round the answer to 3decimal places, if necessary. If there ismore than one critical value, Critical values: (c)Compute the test value. Round the answer to at least 3 decimal places, if necessary. z= Compute the P -value. Round the answer to four decimal places. P-value= (d)Make the decision. What's the null hypothesis? (e)Summarize the…
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what is the test stastic: p value:

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