13 Meaning of Alphais the probability that our confidence interval does not contain the population mean. So is the probability that the confidence interval we construct does contain the true population mean,
14 Finding a 95 % confidence interval for Estimating the mean weight of oranges.Suppose the weights of oranges from a certain orange grove are normally distributed and the population standard deviation is 2.4 ounces. A random sample of size = 36 oranges is selected and the mean weight is determined to be 8.6 ounces.
15 95% confidence intervalKey Fact: Because the weights of oranges are normally distributed, and is 2.4 oz.the distribution of is normal with= and =Why are these statements true?For a normally distributed variable, 95% of the observations will lie within 2 standard deviations of the mean.
16 95% Confidence Interval Thus, a 95% confidence interval for For the normally distributed variable,95% of the sample means, , will fall between2(.4) = .8 of This means that 95% of all samples of size 36 will have the property that the interval from containsthe population mean.This means our sample mean of 8.6 ounces has the property that the interval from to contains the population mean with a probability of 95% .Thus, a 95% confidence interval foris 7.8 to 9.4.
28 What the confidence interval means In the formula for the confidence interval, the sample means will vary. Although the width of the confidence interval remains the same, each confidence interval created will vary according to the variation of the sample mean. However, we can say that, for a confidence level of 95%, 95% of the confidence intervals determined will actually contain For example, out of 20 confidence intervals, 19 of them, on the average will capture and 1 out of 20 will not contain