Assume that you have a sample of n₁ = 8, with the sample mean X₁ = 42, and a sample standard deviation of S₁ = 4, and you have an independent sample of n₂ = 15 from another population with a sample mean of X₂ = 34 and a sample standard deviation of S₂ = 5. What assumptionsabout the two populations are necessary in order to perform the pooled-variance t test for the hypothesis H₁: μ₁ = µ₂ against the alternative H₁: µ₁ > µ₂ and make a statistical decision?Choose the correct answer below.A. It is necessary to assume that the populations from which you are sampling have equal population means and positive standard deviations.B. It is necessary to assume that the populations from which you are sampling have independent normal distributions and equal variances.C. It is necessary to assume that thepopulations from which you are sampling have unequal variances and equal sizes.D. It is necessary to assume that the populations from which you are sampling have negative tSTAT test statistics and unequal sample means.

Assume that you have a sample of n₁ = 8, with the sample mean X1 = 42, and a sample standard…

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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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assume that you have a sample of n1=9, with the sample mean x1=50, and a sample standard deviation of S1=5, and you have an independent sample of n2=15 from another population with a sample mean of X2=31, and the sample deviation S2=7. Construct a 99% confidence interval estimate of the population mean difference between u1 and u2. Assume that the two population variances are equal.
You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1≠μ2Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal. You obtain a sample of size n1=17 with a mean of M1=64.6 and a standard deviation of SD1=11.7 from the first population. You obtain a sample of size n2=17 with a mean of M2=53.2 and a standard deviation of SD2=8.9 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.)
Use the t-distribution and the given 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 distributions are relatively normal. Test Ho : HA = lB vs Ha : HA + HB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (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 = i
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0 : ? H1 : ?
If a researcher obtains a sample mean of M= 54, from a population with u = 46. With a given alpha, which combination of factors is most likely to result in rejecting the null hypothesis?
Two independent samples have been selected, 7777 observations from population 1 and 5858 observations from population 2. The sample means have been calculated to be ?⎯⎯⎯1=13.4x¯1=13.4 and ?⎯⎯⎯2=11.3x¯2=11.3. From previous experience with these populations, it is known that the variances are ?21=27σ12=27 and ?22=29σ22=29. For the hypothesis test of ?0:(?1−?2)=1.8H0:(μ1−μ2)=1.8 and ??:(?1−?2)≠1.8Ha:(μ1−μ2)≠1.8 Use ?=0.04α=0.04. (a) Compute the test statistic. ?=z= (b) Find the approximate p-value?−?????=p−value= The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8. B. We can reject the null hypothesis that (?1−?2)=1.8(μ1−μ2)=1.8 and accept that (?1−?2)≠1.8(μ1−μ2)≠1.8.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a variance of 0.0016 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0 : H1 :
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a variance of 0.0036 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0036 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0:H1:
You wish to test the following claim (H1H1) at a significance level of α=0.005. Ho:μ1=μ2 H1:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=17n1=17 with a mean of M1=52.8M1=52.8 and a standard deviation of SD1=9.4SD1=9.4 from the first population. You obtain a sample of size n2=14n2=14 with a mean of M2=47.4M2=47.4 and a standard deviation of SD2=10.5SD2=10.5 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…
An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 660 days and a variance of 15,625. BIG Corporation claims that the variance of its electric bulbs is less than 15,625. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0: H1:

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