Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 by drawing samples from these values, calculating the mean of each sample, andthen considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll an eight-sided die two times(or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4,5, 6, 7, and 8.The true mean (p) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 isThe number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (8) times the number of possibilities on thesecond roll (also 8), or 8(8) = 64. If you collected all of these possible samples, the mean of your sampling distribution of means (HM) would equal, and the standard deviation of your sampling distribution of means (that is, the standard error or GM) would beThe following chart shows the sampling distribution of the mean (M) for your experiment. Suppose you do this experiment once (that is, you roll thedie two times). Use the chart to determine the probability that the mean of your two rolls is equal to the true mean, or P(M = μ), is▼. Theprobability that the mean of your two rolls is greater than 1.5, or P(M 1.5), isFrequency98765K3210, and the true standard deviation (o) is351.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5M7.0 7.5 8.0 Fertical at a = 0.01 isNow evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a = 0.01, the null hypothesis isYou find that youconclude that the direction that the stroller faces influences a child's expressive vocabulary at 18months.Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM1 M2) is 5.13,so the t test statistic isUse the following tool to find the critical regions for a = 0.01.t DistributionDegrees of Freedom - 21-3.0-2.02500-1.05000500050000.0-0.686 0.000 0.68625001.02.03.0Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.01, the null hypothesis isconclude that the direction the stroller faces influences a child's expressive vocabulary at 18 months.1The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) areYou find that youWhen you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted inconclusion.

Question

Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 by drawing samples from these values, calculating the mean of each sample, andthen considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll an eight-sided die two times(or equivalently, roll two eight-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4,5, 6, 7, and 8.The true mean (p) of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 isThe number of possible different samples (each of size n = 2) is the number of possibilities on the first roll (8) times the number of possibilities on thesecond roll (also 8), or 8(8) = 64. If you collected all of these possible samples, the mean of your sampling distribution of means (HM) would equal, and the standard deviation of your sampling distribution of means (that is, the standard error or GM) would beThe following chart shows the sampling distribution of the mean (M) for your experiment. Suppose you do this experiment once (that is, you roll thedie two times). Use the chart to determine the probability that the mean of your two rolls is equal to the true mean, or P(M = μ), is▼. Theprobability that the mean of your two rolls is greater than 1.5, or P(M > 1.5), isFrequency98765K3210, and the true standard deviation (o) is351.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5M7.0 7.5 8.0 Fertical at a = 0.01 isNow evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a = 0.01, the null hypothesis isYou find that youconclude that the direction that the stroller faces influences a child's expressive vocabulary at 18months.Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM1 M2) is 5.13,so the t test statistic isUse the following tool to find the critical regions for a = 0.01.t DistributionDegrees of Freedom - 21-3.0-2.02500-1.05000500050000.0-0.686 0.000 0.68625001.02.03.0Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.01, the null hypothesis isconclude that the direction the stroller faces influences a child's expressive vocabulary at 18 months.1The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) areYou find that youWhen you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted inconclusion.

Accepted Answer

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