Question

Respond substantively in 100 or more words to this response.

Confidence intervals are used in statistics to show the amount of uncertainty present within a statistic. These intervals are primarily used with a margin of error to outline the predicted range of values. Therefore, confidence intervals are used in statistics to measure uncertainty. Confidence intervals are paramount as they help reduce the level of risks and uncertainties. Notably, they look at the sample size and the potential variations that may exist in a population and offers the possible range that the accurate results may exist. Therefore, the confidence levels are pivotal in overcoming uncertainties and providing reliable results in statistics. Confidence intervals play a crucial role in stimulating the strength of inferential statistics as they provide essential data that shapes the results of a given study. Notably, inferential statistics primarily depend on point estimation, which utilizes confidence intervals and hypothesis testing. Therefore, they stimulate the effective attainment of crucial results in inferential statistics.

Answer 1

A confidence interval estimates are intervals within which the parameter is expected to fall.

The general form of a confidence interval is:

• estimate ± critical value × std.dev of the estimate

Or

• estimate ± margin of error

The margin of error will depend on two factors:

1. The level of confidence which determines the multiplier
2. The value of the standard error

In general terms, for a 95% CI, we say “we are 95% confident that the true population parameter is between the lower and upper calculated values”.

And if we repeat this process many times, 95% of all intervals should, in fact, contain the true value of the parameter.

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