For the independent-measures t test, which of the following describes the pooled variance (whose symbol is )? The difference between the standard deviations of the two samples A weighted average of the two sample variances (weighted by the sample sizes) An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂) The variance across all the data values when both samples are pooled together For the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is )? An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂) The difference between the standard deviations of the two samples The variance across all the data values when both samples are pooled together A weighted average of the two sample variances (weighted by the sample sizes) In calculating , you typically first need to calculate . is the value used in the denominator of the t statistic for the independent-measures t test. Suppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t test to test whether the means of the two independent populations are the same. The following is a table of the information you gather. Fill in any missing values. Sample Size Degrees of Freedom Sample Mean Standard Deviation Sums of Squares Sample 1 n₁ = 11 M₁ = 4.5 s₁ = 5.4 Sample 2 n₂ = 21 M₂ = 3.6 SS₂ = 1,248.2 The pooled variance for your study is . (Note: You are being asked for this value to three decimal places, because you will need to use it in succeeding calculations. For the most accurate results, retain these three decimal places throughout the calculations.) The estimated standard error of the difference in sample means for your study is . The t statistic for your independent-measures t test, when the null hypothesis is that the two population means are the same, is . The degrees of freedom for this t statistic is .

For the independent-measures t test, which of the following describes the pooled variance (whose symbol is )? The difference between the standard deviations of the two samples A weighted average of the two sample variances (weighted by the sample sizes) An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂) The variance across all the data values when both samples are pooled together For the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is )? An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂) The difference between the standard deviations of the two samples The variance across all the data values when both samples are pooled together A weighted average of the two sample variances (weighted by the sample sizes) In calculating , you typically first need to calculate . is the value used in the denominator of the t statistic for the independent-measures t test. Suppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t test to test whether the means of the two independent populations are the same. The following is a table of the information you gather. Fill in any missing values. Sample Size Degrees of Freedom Sample Mean Standard Deviation Sums of Squares Sample 1 n₁ = 11 M₁ = 4.5 s₁ = 5.4 Sample 2 n₂ = 21 M₂ = 3.6 SS₂ = 1,248.2 The pooled variance for your study is . (Note: You are being asked for this value to three decimal places, because you will need to use it in succeeding calculations. For the most accurate results, retain these three decimal places throughout the calculations.) The estimated standard error of the difference in sample means for your study is . The t statistic for your independent-measures t test, when the null hypothesis is that the two population means are the same, is . The degrees of freedom for this t statistic is .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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For the independent-measures t test, which of the following describes the pooled variance (whose symbol is )?

The difference between the standard deviations of the two samples

A weighted average of the two sample variances (weighted by the sample sizes)

An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂)

The variance across all the data values when both samples are pooled together

For the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is )?

An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂)

The difference between the standard deviations of the two samples

The variance across all the data values when both samples are pooled together

A weighted average of the two sample variances (weighted by the sample sizes)

In calculating , you typically first need to calculate . is the value used in the denominator of the t statistic for the independent-measures t test.

Suppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t test to test whether the means of the two independent populations are the same. The following is a table of the information you gather. Fill in any missing values.

	Sample Size	Degrees of Freedom	Sample Mean	Standard Deviation	Sums of Squares
Sample 1	n₁ = 11		M₁ = 4.5	s₁ = 5.4
Sample 2	n₂ = 21		M₂ = 3.6		SS₂ = 1,248.2

The pooled variance for your study is . (Note: You are being asked for this value to three decimal places, because you will need to use it in succeeding calculations. For the most accurate results, retain these three decimal places throughout the calculations.)

The estimated standard error of the difference in sample means for your study is .

The t statistic for your independent-measures t test, when the null hypothesis is that the two population means are the same, is .

The degrees of freedom for this t statistic is .

Expert Solution

Step 1

For the independent-measures t test, which of the following describes the pooled variance ${s_{p}}^{2}$ :

A weighted average of the two sample variances (weighted by the sample sizes)

It is given by the formula:

${s_{p}}^{2} = \frac{(n_{1} - 1) {s_{1}}^{2} + (n_{2} - 1) {s_{2}}^{2}}{n_{1} + n_{2} - 2}$

For the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means: $M_{1} - M_{2}$ :

An estimate of the standard distance between the difference in sample means (M₁ – M₂) and the difference in the corresponding population means (μ₁ – μ₂)

In calculating the estimated standard error $M_{1} - M_{2}$ , you typically first need to calculate the pooled variance. The estimated standard error $M_{1} - M_{2}$ is the value used in the denominator of the t statistic for the independent-measures t test.

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