L3. The following table lists (1 - a)-quantiles of N(0, 1), commonly used in hypothesis tests:10% 5% 2.5% 1%1.282 1.645 1.960 2.326aqaThese values were obtained using the qnorm () function in R. Test the following hypothesesat 5% level, assuming that the data are normally distributed with the given variances:i) o² = 4, n= = 16, x = 2.9, Ho: μ = 2.ii) o² = 4, n = = 16, x = 2.9, Ho: µ ≤ 2.iii) o² = 2, nxiv)= = 10, x = -0.3o² = 3, ny = 20, y = 0.2Ho: |x = [y•= 2, nx = 10, x= -0.3= 20, y = 0.2= 3, nyHo: μα < My·

Given. List of (1-alpha ) quantiles of the standard normal variate, at 1%,2.5%,5%, and 10% To test…

Answered: These values were obtained using the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, X2, .. ., Xn be a random sample from a normal distribution with mean u and variance o?. Find an estimator for o? using the method of moments. Is this estimator bi- ased/unbiased? Is it consistent?
Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel. (a-1) Comparison of GPA for randomly chosen college juniors and seniors: x⎯⎯1x¯1 = 4.5, s1 = .20, n1 = 15, x⎯⎯2x¯2 = 4.9, s2 = .30, n2 = 15, α = .025, left-tailed test.(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.) d.f. Not attempted t-calculated Not attempted p-value Not attempted t-critical Not attempted (a-2) Based on the above data choose the correct decision. Do not reject the null hypothesis Reject the null hypothesis
You wish to test the following claim (HaHa) at a significance level of α=0.05 Ho:μ1=μ2 Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, assume that the variances of the two populations are equal. You obtain a sample of size n1=23 with a mean of ¯x1=74.5 and a standard deviation of SD1=20.4 from the first population. You obtain a sample of size n2=11with a mean of ¯x2=89.8and a standard deviation of SD2=7.3 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of…
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.)
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A researcher decides to measure anxiety in group of bullies and a group of bystanders using a 23-item, 3 point anxiety scale. Assume scores on the anxiety scales are normally distributed and the variance among the group of bullies and bystanders are the same. A group of 30 bullies scores an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. A group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 8 on the anxiety scale. You do not have any presupposed assumptions whether bullies or bystanders will be more anxious so you formulate the null and alternative hypothesis based on that.
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