Estimation and Hypothesis Testing for Two Population Parameters
PPT
VIDEO
24. Hypothesis Testing for Two Population Variances
Hypothesis testing 2 L06
L-4
Proportion Hypothesis Testing, example 2
Testing of hypothesis Mean of two Population|Statistical Inference| MAT202 |MAT208 |Module 3| Part 9
Hypothesis Test for a Population Mean. P-Value Method. Two-Sided T-Test w/ Pop St Dev. Unknown
COMMENTS
10.29: Hypothesis Test for a Difference in Two Population Means (1 of 2
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Hypothesis Test for a Difference in Two Population Means (1 of 2
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Hypothesis Testing: 2 Means (Independent Samples)
Inference for Comparing 2 Population Means (HT for 2 Means, independent samples) More of the good stuff! We will need to know how to label the null and alternative hypothesis, calculate the test statistic, and then reach our conclusion using the critical value method or the p-value method. ... Hypothesis Testing, and then Mean Two Independent ...
10.2: Two Population Means with Unknown Standard Deviations
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch \(t\)-test. The degrees of freedom formula was developed by Aspin-Welch. ... {2}\) Null hypothesis: the means of the final exam scores are equal for the online and face-to-face statistics classes. \(H_{a ...
10: Hypothesis Testing about Two Population Means and Proportions
10.2: Hypothesis Testing with Two Samples. You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. To compare two means or two proportions, you work with two groups. The groups are classified either as independent ...
10.2: Comparing Two Independent Population Means
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t t -test. The degrees of freedom formula we will see later was developed by Aspin-Welch. When we developed the hypothesis test for the mean and proportions we began with the Central Limit Theorem.
11.3: Two Population Means with Known Standard Deviations
Test at a 5% level of significance. Answer. This is a test of two independent groups, two population means, population standard deviations known. Random Variable: X¯1 −X¯2 = X ¯ 1 − X ¯ 2 = difference in the mean number of months the competing floor waxes last. H0: μ1 ≤ μ2 H 0: μ 1 ≤ μ 2. Ha: μ1 > μ2 H a: μ 1 > μ 2.
7.3
We are 99% confident that the difference between the two population mean times is between -2.012 and -0.167. ... The same process for the hypothesis test for one mean can be applied. The test for the mean difference may be referred to as the paired t-test or the test for paired means.
Testing for Two Population Means
The degrees of freedom formula was developed by Aspin-Welch. The comparison of two population means is very common. A difference between the two samples depends on both the means and the standard deviations. Very different means can occur by chance if there is great variation among the individual samples. In order to account for the variation ...
10.2: Two Population Means with Known Standard Deviations
This is a test of two independent groups, two population means. The population standard deviations are unknown, but the sum of the sample sizes is 30 + 30 = 60, which is greater than 30, so we can use the normal approximation to the Student's-t distribution. Subscripts: 1: Democratic senators 2: Republican senators.
Hypothesis Test for a Difference in Two Population Means (1 of 2)
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Hypothesis Test for a Difference in Two Population Means (2 of 2
Her hypothesis is that the mean scores for males and females will differ, but she does not have an opinion about which population will have a higher mean score. Here are her hypotheses. H 0: μ 1 - μ 2 = 0. H a: μ 1 - μ 2 ≠ 0. We can also write the hypotheses as follows. H 0: μ 1 = μ 2. H a: μ 1 ≠ μ 2. She chose a random sample ...
9.3 Statistical Inference for Two Population Means with Unknown
The hypothesis test for the difference in two independent population means with unknown population standard deviations is a well established process: Write down the null and alternative hypotheses in terms of the differences in the population means [latex]\mu_1-\mu_2[/latex].
Two Population Calculator with Steps
This is a simple extension of the formula for the one population case. In the one population case the degrees of freedom is given by df = n - 1. If we add up the degrees of freedom for the two samples we would get df = (n1 - 1) + (n2 - 1) = n1 + n2 - 2. This formula gives a pretty good approximation of the more complicated formula above.
Hypothesis Testing for 2 Samples: Introduction
The mean for the last recorded percentage was less than half of the initial score: 30.27 (SD 34.03). The decrease was found to be statistically significant using a paired sample t-test (t = 4.36, 36 df, p < .001).". This is a hypothesis test for matched pairs, sometimes known as 2 means, dependent samples.
3.2 Two population means
3.2. Two population means. The procedure for testing hypotheses about two population means is similar to the procedure for a single population mean. The null hypothesis states that there is no difference between two population means μ1 μ 1 and μ2 μ 2: H0: μ1 = μ2 (3.6) (3.6) H 0: μ 1 = μ 2.
Estimating the Difference in Two Population Means
Hypothesis Test for a Population Mean (2 of 5) Hypothesis Test for a Population Mean (3 of 5) Hypothesis Test for a Population Mean (4 of 5) ... Confidence Interval to Estimate μ 1 − μ 2. In a hypothesis test, when the sample evidence leads us to reject the null hypothesis, we conclude that the population means differ or that one is larger ...
9.3: Comparison of Two Population Means
Standardized Test Statistic for Hypothesis Tests Concerning the Difference Between Two Population Means: Paired Difference Samples. T = d¯ −D0 sd/ n−−√ T = d ¯ − D 0 s d / n. where there are n n pairs, d¯ d ¯ is the mean and sd s d is the standard deviation of their differences. The test statistic has Student's t t -distribution ...
9.2: Comparing Two Independent Population Means (Hypothesis test)
This page titled 9.2: Comparing Two Independent Population Means (Hypothesis test) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
10.2: Two Population Means with Known Standard Deviations
A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations), will have these characteristics: Random variable:
Hypothesis Test for a Population Mean (2 of 5)
In 2 of the 3 samples, we also see outliers, just as we see in the population. So by looking at the sample, we can get a pretty good sense that the variable is not normally distributed in the population. In this example, the sample size is less than 30. We can use the t-test only if the variable is normally distributed in the population.
10.26: Hypothesis Test for a Population Mean (5 of 5)
The mean pregnancy length is 266 days. We test the following hypotheses. H 0: μ = 266. H a: μ < 266. Suppose a random sample of 40 women who smoke during their pregnancy have a mean pregnancy length of 260 days with a standard deviation of 21 days. The P-value is 0.04.
Hypothesis Test for a Population Mean (1 of 5)
In "Hypothesis Test for a Population Mean," we learn to use a sample mean to test a hypothesis about a population mean. We did hypothesis tests in earlier modules. In Inference for One Proportion, each claim involved a single population proportion. In Inference for Two Proportions, the claim was a statement about a treatment effect or a ...
IMAGES
VIDEO
COMMENTS
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Inference for Comparing 2 Population Means (HT for 2 Means, independent samples) More of the good stuff! We will need to know how to label the null and alternative hypothesis, calculate the test statistic, and then reach our conclusion using the critical value method or the p-value method. ... Hypothesis Testing, and then Mean Two Independent ...
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch \(t\)-test. The degrees of freedom formula was developed by Aspin-Welch. ... {2}\) Null hypothesis: the means of the final exam scores are equal for the online and face-to-face statistics classes. \(H_{a ...
10.2: Hypothesis Testing with Two Samples. You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. To compare two means or two proportions, you work with two groups. The groups are classified either as independent ...
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t t -test. The degrees of freedom formula we will see later was developed by Aspin-Welch. When we developed the hypothesis test for the mean and proportions we began with the Central Limit Theorem.
Test at a 5% level of significance. Answer. This is a test of two independent groups, two population means, population standard deviations known. Random Variable: X¯1 −X¯2 = X ¯ 1 − X ¯ 2 = difference in the mean number of months the competing floor waxes last. H0: μ1 ≤ μ2 H 0: μ 1 ≤ μ 2. Ha: μ1 > μ2 H a: μ 1 > μ 2.
We are 99% confident that the difference between the two population mean times is between -2.012 and -0.167. ... The same process for the hypothesis test for one mean can be applied. The test for the mean difference may be referred to as the paired t-test or the test for paired means.
The degrees of freedom formula was developed by Aspin-Welch. The comparison of two population means is very common. A difference between the two samples depends on both the means and the standard deviations. Very different means can occur by chance if there is great variation among the individual samples. In order to account for the variation ...
This is a test of two independent groups, two population means. The population standard deviations are unknown, but the sum of the sample sizes is 30 + 30 = 60, which is greater than 30, so we can use the normal approximation to the Student's-t distribution. Subscripts: 1: Democratic senators 2: Republican senators.
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of "no effect" or "no difference.". H 0: μ 1 - μ 2 = 0, which is the same as H 0: μ 1 = μ 2. The alternative hypothesis, H a ...
Her hypothesis is that the mean scores for males and females will differ, but she does not have an opinion about which population will have a higher mean score. Here are her hypotheses. H 0: μ 1 - μ 2 = 0. H a: μ 1 - μ 2 ≠ 0. We can also write the hypotheses as follows. H 0: μ 1 = μ 2. H a: μ 1 ≠ μ 2. She chose a random sample ...
The hypothesis test for the difference in two independent population means with unknown population standard deviations is a well established process: Write down the null and alternative hypotheses in terms of the differences in the population means [latex]\mu_1-\mu_2[/latex].
This is a simple extension of the formula for the one population case. In the one population case the degrees of freedom is given by df = n - 1. If we add up the degrees of freedom for the two samples we would get df = (n1 - 1) + (n2 - 1) = n1 + n2 - 2. This formula gives a pretty good approximation of the more complicated formula above.
The mean for the last recorded percentage was less than half of the initial score: 30.27 (SD 34.03). The decrease was found to be statistically significant using a paired sample t-test (t = 4.36, 36 df, p < .001).". This is a hypothesis test for matched pairs, sometimes known as 2 means, dependent samples.
3.2. Two population means. The procedure for testing hypotheses about two population means is similar to the procedure for a single population mean. The null hypothesis states that there is no difference between two population means μ1 μ 1 and μ2 μ 2: H0: μ1 = μ2 (3.6) (3.6) H 0: μ 1 = μ 2.
Hypothesis Test for a Population Mean (2 of 5) Hypothesis Test for a Population Mean (3 of 5) Hypothesis Test for a Population Mean (4 of 5) ... Confidence Interval to Estimate μ 1 − μ 2. In a hypothesis test, when the sample evidence leads us to reject the null hypothesis, we conclude that the population means differ or that one is larger ...
Standardized Test Statistic for Hypothesis Tests Concerning the Difference Between Two Population Means: Paired Difference Samples. T = d¯ −D0 sd/ n−−√ T = d ¯ − D 0 s d / n. where there are n n pairs, d¯ d ¯ is the mean and sd s d is the standard deviation of their differences. The test statistic has Student's t t -distribution ...
This page titled 9.2: Comparing Two Independent Population Means (Hypothesis test) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations), will have these characteristics: Random variable:
In 2 of the 3 samples, we also see outliers, just as we see in the population. So by looking at the sample, we can get a pretty good sense that the variable is not normally distributed in the population. In this example, the sample size is less than 30. We can use the t-test only if the variable is normally distributed in the population.
The mean pregnancy length is 266 days. We test the following hypotheses. H 0: μ = 266. H a: μ < 266. Suppose a random sample of 40 women who smoke during their pregnancy have a mean pregnancy length of 260 days with a standard deviation of 21 days. The P-value is 0.04.
In "Hypothesis Test for a Population Mean," we learn to use a sample mean to test a hypothesis about a population mean. We did hypothesis tests in earlier modules. In Inference for One Proportion, each claim involved a single population proportion. In Inference for Two Proportions, the claim was a statement about a treatment effect or a ...