= 3 versusExample: In a two sample test of Ho: ₁-2H₁₁-23, suppose that the data are normal, m = nand o² = 0 = 84.0. Can we choose m such that the testhas level a = 0.01 and 3 = 0.05 at 1₁ - ₂ : 5.0? Thisquestion concerns experimental design.

Solution: From the given information, Null hypothesis: Alternative hypothesis: The data follows…

Answered: Example: In a two sample test of Ho:…

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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A researcher surveyed randomly selected Democrats and Republicans asking them what the number one concern should be for the president of the United States. The results of the survey are shown below. Is there evidence to conclude that there is a difference in what Democrats and Republicans think is the most important? Frequencies of Concerns for Democrats and Republicans Economy Foreign Affairs Family Values Environment Other Democrats 95 40 96 72 39 Republicans 97 71 114 45 39 What can be concluded at the αα = 0.05 significance level? What is the correct statistical test to use? Homogeneity Independence Paired t-test Goodness-of-Fit What are the null and alternative hypotheses?H0:H0: Political affiliation and number one concern are dependent. Political affiliation and number one concern are independent. The distribution of concerns for Democrats is the same as it is for Republicans. The distribution of concerns for Democrats is not the same as it is for…
You wish to test the following claim (HaHa) at a significance level of α=0.01 Ho:μ1=μ2 Ha:μ1≠μ2 You 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=20 with a mean of ¯x1=55.2 and a standard deviation of SD1=11.3 From the first population. You obtain a sample of size n2=18n2=18 with a mean of ¯x2=48.3 and a standard deviation of SD2=7.2 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…
Suppose we are conducting the following hypothesis test at the 10% significance level. HO: µ1 - u2 = 0 Ha: µ1 - µ2 < 0 Assume equal population variances. If n = 9 and n2 = 7, what critical value forms the rejection region? %3D O t= -1.345 O z = 1.28 O t= 1.345 O z = -1.28
A test of H0: μ = 50 versus H1: μ ≠ 50 is performed using a significance level of α = 0.01. The value of the test statistic is z = 1.23. a. .Is H0 rejected?
Are Republicans less likely than Democrats to display the American flag in front of their residence on the Fourth of July? 428 of the 693 Republicans surveyed display the flag on the Fourth of July and 471 of the 714 Democrats surveyed display the flag on the Fourth of July. What can be concluded at the αα = 0.10 level of significance? 1. For this study, we should use? Select an answer: z-test for a population proportion? z-test for the difference between two population proportions? t-test for the difference between two independent population means? t-test for the difference between two dependent population means? or t-test for a population mean ? 2. The null and alternative hypotheses would be: H0? Select an answer: p1 or μ1? Select an answer > , ≠, =, or < ? Select an answer: μ2 or p2 ? (please enter a decimal) H1? Select an answer: p1or μ1? Select an answer: =, <, ≠, or > ? Select an answer: p2 or μ2 ? (Please enter a decimal) 3. The test statistic:…
2. V is completely known (i.e., the values of all elements of V are given). Construct an estimator of ? and discuss the statistical properties (e.g., bias, variance) of your estimator.
For the model Y = Bo + B1X1 + B2X2+ B3X3 + B4X4+ ɛ. When testing Ho: B3 = 0 vs. Ha: B3 + 0 at a = 0.05 We get a test statistic value of tcal = 3.24. If sample size n = 10, what is the critical value for this test? O 2.093 O 2.571 O 3.182 O 2.228
Specific Motors of Detroit has developed a new automobile known as the M car. 24 M cars and 28 J cars (from Japan) were road tested to compare miles-per-gallon (mpg) performance. sample 1 (M cars) : n1 = 24, X ̄1 = 29.8, s1 = 2.56 sample 2 (J cars) : n2 = 28, X ̄2 = 27.3, s2 = 1.81 (b) Can we conclude, using a .05 level of significance, that the miles-per-gallon (mpg) performance of M cars is greater than the miles-per-gallon performance of J cars? (d) Find the critical values. (e) Rejection region and conclusion. (f) Interpret the results.
A sociologist is investigating the relationship between job satisfaction and work-life balance. For a sample of 18 individuals, the following data is obtained: Job Satisfaction: M = 4.0 SS = 16.0 Work-Life Balance: M = 6.0 SS = 134.0 SP = 32.0 r= .69 d. Conduct a hypothesis test using an alpha level of α = .01 to determine if the correlation is significant. Include all steps.
The appearance of leaf pigment glands in the seedling stage of cotton plants is genetically controlled. According to one theory of the control mechanism, the population ratio of glandular to glandless plants resulting from a certain cross should be 11.5, according to another it should be 13:3. In one experiment, the cross produced 89 glandular and 36 glandless plants. Use goodness-of-fit tests (at alpha= 0.10) to determine whether the data is consistent with a) the 11:5 theory, ar b) the 13:3 theory.
It is desired to test Ho: 50 against Ho: 50, using a sample size of n = 13 from a normal population with mean and variance ². Suppose that the true mean is = 50 +0.75 a Which one of the following statements is incorrect? O a. O b. O C. O d. O a. O b. O c Hypotheses: Ho: μ = 50 against Ho:μ + 50. In a random sample of 36 observations from a bivariate normal distribution, it was found that the sample correlation coefficient r = 0.4. If we want to test the significance of the correlation at the 5% level of significance, which one of the following statements is incorrect? O d. The probability of type 2 error at the 5% level of significance is 0.69. The probability of type I error at the 5% level significance is 0.31. The power of the test at the 5% level of significance is 0.35. Ho: p=0 against Ho: p0. T = 2.5448. The critical value is 2.032. We do not reject H, at the 5% level of significance. Let Y, and Y₂ be independent random variables such that E(Y₂) 0₁ E(₂) 0₂ and VAR(Y) =VAR(₂)= ².…
In a study of the effects on babies of cocaine use during pregnancy, the following data on birth weights were obtained: n = 190, x with a bar above it = 2700 g, s = 645g (according to data from "Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure ”, by Singer et al., Journal of the American Medical Association, vol. 291, no. 20). The study design justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct an estimate of the 95% confidence interval for m, the mean birth weight of all babies born to mothers who used cocaine during pregnancy.

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Example: In a two sample test of Ho: ₁-2 = 3 versus H₁₁-23, suppose that the data are normal, m = n and o=o= 84.0. Can we choose m such that the test = 5.0? This has level a = : 0.01 and 3 = 0.05 at μ₁ −µ₂ question concerns experimental design.