Standard Error of the Mean. This equation implies that sampling error decreases as sample size increases. This is important because it suggests that if we want to make sampling error as small as possible, we need to use as large of a sample size as we can manage. Standard Error of the Mean.
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The area under a normal curve
Mu = 3.6
SE = .5
3.6 – 1.96 .5 = 2.62
3.6 + 1.96 .5 = 4.58
Thus, the 95% confidence interval ranges from 2.62 to 4.58. Under the sampling conditions described, 95% of the time we will observe sample means between 2.62 and 4.58.
n = 7
mean of sample means = 3.6
SD of sample means = .5
.98 (unadjusted sample mean) vs. (4.8/4) = 1.2 (adjusted sample mean)
In forward inference, we can say that this method of constructing intervals will capture the observed sample mean 95% of the time.
In backwards inference, we can say that this method of constructing intervals will capture the population mean 95% of the time.