Explain the circumstances under which we would need to pool the variance for an independent samples t-test

Q: Briefly explain the effect of non-homogeneity of variance in one-way analysis of variance in both…

A: Introduction: Suppose there are k groups. Denote the true average of each of the k groups as μ1, μ2,…

Q: How did we use Cochran's Theorem to develop inference procedures for variances? What kind of data…

A: Cochran's theorem is used to establish the results which is relating to the probability…

Q: The omnibus null hypothesis when performing an analysis of variance is that there are differences…

A: In general, the omnibus null hypothesis states that all the group means are the same, which mean…

Q: Question 18

A: The independent t-test assumes the variances of the two groups we are measuring are equal in the…

Q: a. Which if these estimators are unbiased for 6? b. Among the unbiased estimators, which has the…

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Q: 10. A manufacturer is testing its new grain moisture meter and sampled out 5 grain types (A, B, C,…

A: Given information: Sample  MC A 9.6   9.8   9.7 B 12.8   12.9   12.7 C 16.8…

Q: The data from an independent-measures research study produce a sample mean difference of 4 points…

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Q: What is sample variance?

A: In very simple words, Sample variance means the variability in the sample around its average value.…

Q: Two balanced coins are flipped. What is the variance of the number of heads observed?

A: For this case, the number of possible outcomes will be:  (HH), (HT), (TT), (TH) Here, H represents…

Q: True or False In general, a sample with a large variance is more likely to produce a significant…

A: Note that as the variance increases, p-value also tends to increase. To produce a significant…

Q: A quality-control manager was concerned about variability in the amount of an active ingredient in…

A: Given data: Sample size = 21 To find: What is the probability that the sample variance of the amount…

Q: What is the variance of number of Sundays on a nonleap year?

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Q: What is formula for variance for sample?

A: Variance measures absolute variability in a data set, calculated with respect to the mean. That is,…

Q: By what numerical value should SS be divided in order to compute an unbiased variance?

A: The variance is obtained using ratio of squared deviations and sample size.

Q: The analysis of variance (ANOVA) can be used for comparing the equality of more than two treatment…

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Q: A pooled variance estimate is useful for two-sample hypothesis tests of a normal mean when the…

A: It is given that the population variances are equal.

Q: When performing a two-sample t-test, if the variance in the two groups being compared are considered…

A: 2 sample test is used to compare the means of 2 samples. t-test is a parametric test.

Q: 4. Describe the homogeneity of variance assumption and explain why it is inportant for the…

A: Homogeneity of variance states that the variance in each group should be equal (or homogeneous).…

Q: An analysis of variances produces dftotal = 33 and dfwithin = 30. For this analysis, how many…

A: Given:  Degrees of freedom total =33 and degrees of freedom within=30  Then to find nonof treatment…

Q: What are some assumptions researchers may have about a related-samples t-test?

A: Correlated samples t-test or matched pairs t-test or repeated measures t-test: The paired t-test or…

Q: If homogeneity of variance is violated for a correlated-groups t-test, what nonparametric test…

A: Introduction: A correlated-groups t-test, also known as the paired t-test, is used to compare…

Q: Describe research situation to illustrate the use of the One-way Analysis of Variance and one…

A: We know that, Assumptions of One-way analysis of variance (ANOVA) : 1] Samples are randomly…

Q: Compute the coefficient of variation for population mean = 20 and population variance = 2

A: The population mean is 20 and the population standard deviation is 2.

Q: Why is the unbiased estimator of variance used?

A: the unbiased estimator of the population variance, corrects the tendency of the sample variance to…

Q: When conducting a One-Way Analysis of variance, what option on the LSMEANS statement requests a…

A: One way analysis of variance ( ANOVA ) compares the means of two or more independent groups in order…

Q: The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η,…

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Q: what is the general alternative hypothesis for a two tailed independent samples t test

A: Null and alternative hypotheses: The hypothesis, which is pre assumed as true, tentatively settled…

Q: What is the best point estimate for the population's variance if the sample variance is 41?

A: Given,sample variance(s2)=41

Q: If the variability between the different sample means taken from the same population is small, we…

A: If the variability between the different sample means taken from the same population is small, we…

Q: Prove that the sample variance is an unbiased estimator for the population variance. That is, show…

A: Let X1 , X2........Xn be the independent observations from a population with mean μ and variance σ2…

Q: The data from an independent-measures research study produce a sample mean difference of 4 points…

A:

Q: What do we call variance in the ANOVA equation, and what notation do we use to represent them?

A: Given information: The information about ANOVA is given.

Q: To test if there is a difference in the population variances, the appropriate degrees of freedom (in…

A: Note : Since you have asked multiple questions, we will solve the first question for you. If you…

Q: How, in general, is the requirement of equal population variances to allow the use of analysis of…

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Q: t-statistic,

A: Let we have to write the value of t statistics  from the ANOVA table above given all the values…

Q: Perform the analysis of variance (ANOVA) at the 5% significance level to identify is there any…

A: Excel Procedure: Enter the data for 1, 2, 3 in Excel sheet>Go to Data Menu>Click on Data…

Q: For an analysis of variance comparing four treatments, MSpetween = 12. What is the value of…

A: Given: MS between=12 Total number of treatments = k = 4 The between degrees of freedom can be…

Q: If other factors are held constant, increasing the sample variances will have very little influence…

A: Effect size : The size of the effect indicates how significant the association between variables or…

Q: Why is it impossible to calculate a negative F value when using an Analysis of Variance to test a…

A: According to the F statistic for ANOVA,  MST =Mean square of treatment MSE = Mean square error In…

Q: a population with a known mean but an unknown variance.

A: We have to study a single sample's mean is being compared to the population with a known mean but…

Q: How to get rid of co-variances double head arrows among the demographic variables in semplot…

A: R- lavaan is an open-source package in R programming for latent variable modelling.

Q: Two samples each with n =5 scores has a pooled variance = 40. What is the estimated standard error…

A: The formula of the estimated standard error for the sample mean difference is,

Q: What is the relationship between the sampling variance of an OLS parameter estimate, and the total…

A: Sampling variance is the variance of the sampling distribution for a random variable. It measures…

Q: Provide one sample problem of Analysis of Variance (ANOVA)

A: ANOVA or the Analysis of Variance, is the process of comparing more than two samples and their…

Q: Suppose a sample 30 observations is drawn from a population with variance population with variance…

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Q: If, in an analysis of variance, you find that MSTR is greater than MSE, why can you not immediately…

A: While performing Analysis of Variance (ANOVA), we calculate the test statistics which is the ratio…

Q: the homogeneity of variances assumption states that the variance in the two samples must be equal?…

A: Homogeneity of variances always make about the population variance not about sample.