Confidence Interval Standard Error Of The Mean
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normal distribution calculator to find the value of z to use for a confidence interval Compute a confidence interval on the mean when σ is known Determine whether to use a t 95 confidence interval standard error distribution or a normal distribution Compute a confidence interval on the mean how does standard error related to confidence interval when σ is estimated View Multimedia Version When you compute a confidence interval on the mean, you compute the lower limit of the 95 confidence interval mean of a sample in order to estimate the mean of the population. Clearly, if you already knew the population mean, there would be no need for a confidence interval. However,
Confidence Interval Standard Error Of Measurement
to explain how confidence intervals are constructed, we are going to work backwards and begin by assuming characteristics of the population. Then we will show how sample data can be used to construct a confidence interval. Assume that the weights of 10-year-old children are normally distributed with a mean of 90 and a standard deviation of 36. What is the sampling distribution confidence interval standard error or standard deviation of the mean for a sample size of 9? Recall from the section on the sampling distribution of the mean that the mean of the sampling distribution is μ and the standard error of the mean is For the present example, the sampling distribution of the mean has a mean of 90 and a standard deviation of 36/3 = 12. Note that the standard deviation of a sampling distribution is its standard error. Figure 1 shows this distribution. The shaded area represents the middle 95% of the distribution and stretches from 66.48 to 113.52. These limits were computed by adding and subtracting 1.96 standard deviations to/from the mean of 90 as follows: 90 - (1.96)(12) = 66.48 90 + (1.96)(12) = 113.52 The value of 1.96 is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean; 12 is the standard error of the mean. Figure 1. The sampling distribution of the mean for N=9. The middle 95% of the distribution is shaded. Figure 1 shows that 95% of the means a
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Margin Of Error Confidence Interval
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Sampling Error Confidence Interval
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