# Question: We discussed how to use summary statistics sample sizes sample

We discussed how to use summary statistics (sample sizes, sample means, and sample standard deviations) to conduct a one-way ANOVA.

a. Verify the formula presented there for obtaining the mean of all the observations, namely,

b. Show that, if all the sample sizes are equal, then the mean of all the observations is just the mean of the sample means.

c. Explain in detail how to obtain the value of the F-statistic from the summary statistics. Confidence Intervals in One-Way ANOVA. Assume that the conditions for one-way ANOVA are satisfied, and let s = √ MSE. Then we have the following confidence-interval formulas.

• A (1 − α)-level confidence interval for any particular population mean, say, μi , has endpoints

• A (1 − α)-level confidence interval for the difference between any two particular population means, say, μi and μj , has endpoints

In both formulas, df = n − k, where, as usual, k denotes the number of populations and n denotes the total number of observations.

a. Verify the formula presented there for obtaining the mean of all the observations, namely,

b. Show that, if all the sample sizes are equal, then the mean of all the observations is just the mean of the sample means.

c. Explain in detail how to obtain the value of the F-statistic from the summary statistics. Confidence Intervals in One-Way ANOVA. Assume that the conditions for one-way ANOVA are satisfied, and let s = √ MSE. Then we have the following confidence-interval formulas.

• A (1 − α)-level confidence interval for any particular population mean, say, μi , has endpoints

• A (1 − α)-level confidence interval for the difference between any two particular population means, say, μi and μj , has endpoints

In both formulas, df = n − k, where, as usual, k denotes the number of populations and n denotes the total number of observations.

## Answer to relevant Questions

The data on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions are presented in the following table. a. Find and interpret a 95% confidence interval for the mean ...a. Obtain individual normal probability plots and the standard deviations of the samples. b. Perform a residual analysis. c. Decide whether presuming that the assumptions of normal populations and equal standard deviations ...State the four assumptions for one-way ANOVA, and explain how those assumptions can be checked. Ha: ρ ≠ 0 Specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the null hypothesis in favor of the ...Following are the data on age of fetuses and length of crown-rump from Exercise. At the 10% significance level, do the data provide sufficient evidence to conclude that age and crown-rump length are linearly correlated? ...Post your question