This is the average of the averages, and it is the best. We can simply calculate the lower an upper limits of our 99% confidence interval. The centerline of the X-bar chart, is also called the grand average, and is also called X-double bar. Now that the margin of error has been calculated. Once steps #1 - #3 from above are completed, we can then calculate z* and the margin of error as shown below: > # Calculate z* for 99% confidence intervalģ. Next we will calculate the test statistic using the following formula: It should be clear that this distribution is skewed right as the smallest possible value is a household of 1 person but the largest households can be very large indeed. Next we will calculate the mean and standard error: > # Calculate statistics of dataĤ. EXAMPLE 10: Using the Sampling Distribution of x-bar Household size in the United States has a mean of 2.6 people and standard deviation of 1.4 people. We will begin by defining the null and alternative hypthesis.Ĭonclusion: Given the small sample size, and the fact that there are no extreme outliers, we will conclude that the data is drawn from a population that is normally distributed.ģ. The mean of a sampling distribution of the means (called mu x bar) is always equal to the mean of the parent population.
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