# Confidence Intervals

**Topics:**Sample size, Normal distribution, Standard deviation

**Pages:**3 (917 words)

**Published:**November 11, 2012

The confidence intervals represent upper and lower bounds of variation around each reference forecast. Values may occur outside the confidence intervals due to external shocks, such as extreme weather, structural changes to the economic system, geopolitical events, or technology development. The confidence intervals increase in width throughout the forecast period due to the increasing level of uncertainty in each subsequent year. The upper and lower bounds were based on one to two standard deviations of the historic values, indicating at least a 68 percent probability that future values would be expected to fall within the confidence interval. The confidence interval for the first forecast year is based on one standard deviation and grows linearly until it reaches two standard deviations, or a 95 percent probability.

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For example, if we have polled a number of respondents from the home owners let’s say 3500 respondents, and from those only 1190 are using electricity to heat their homes, this means that 34.0% are using electricity to heat their homes,

p̂ = 1190/3500 = 34.0%.

And we know that a second sample of 3500 home owners wouldn’t have a sample proportion of exactly 34.0%. If another group of home owners has taken and we found that they have a sample of proportion of 38.0%, So the sampling proportion will be the key to our ability to generalize from our sample to the population.

Now, we know that the sampling distribution model is centered at the true proportion, p, of all home owners who use electricity to heat their homes. But we don’t know p. it isn’t 34.0%. That’s the p̂ from our sample. What we do know is that the sampling distribution model of p̂ centered at p, and we know that the standard deviation of the sampling distribution is

SE(p̂) = √ p̂ q̂/n = √(.34)(1-.34)/3500 = 0.008

Because our sample (3500) is...

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