Confidence Interval (Women's Heights) Quiz

PDF page 480: • The student will calculate a 90% confidence interval using the given data.

PDF page 480: known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of ten values. Write the confidence interval you obtained in the first space of Table 8.9.

PDF page 480: Table 8.8 Heights of 100 Women (in

PDF page 481: intervals, count how many of them contain the population mean μ; i.e., for how many intervals does the value of μ lie between the endpoints of the confidence interval?

PDF page 482: Confidence Interval (CI) an interval estimate for an unknown population parameter. This depends on:

PDF page 482: Confidence Interval (CI) an interval estimate for an unknown population parameter. This depends on:

PDF page 482: • the sample and its size.

PDF page 482: Confidence Level (CL) the percent expression for the probability that the confidence interval contains the true population parameter; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Degrees of Freedom (df) the number of objects in a sample that are free to vary Error Bound for a Population Mean (EBM) the margin of error; depends on the confidence level, sample size, and known or estimated population standard deviation. Error Bound for a Population Proportion (EBP) the margin of error; depends on the confidence level, the sample size, and the estimated (from the sample) proportion of successes. Inferential Statistics also called statistical inference or inductive statistics; this facet of statistics deals with estimating a population parameter based on a sample statistic. For example, if four out of the 100 calculators sampled are defective we might infer that four percent of the production is defective. 2 2 Normal Distribution – (x – μ) σ / 2

PDF page 483: standard deviation is known. When estimating a population mean, the margin of error is called the error bound for a population mean (EBM). A confidence interval has the general form: (lower bound, upper bound) = (point estimate – EBM, point estimate + EBM) The calculation of EBM depends on the size of the sample and the level of confidence desired. The confidence level is the percent of all possible samples that can be expected to include the true population parameter. As the confidence level increases, the corresponding EBM increases as well. As the sample size increases, the EBM decreases. By the central limit theorem, σ EBM = z n Given a confidence interval, you can work backwards to find the error bound (EBM) or the sample mean. To find the error bound, find the difference of the upper bound of the interval and the mean. If you do not know the sample mean, you can find the error bound by calculating half the difference of the upper and lower bounds. To find the sample mean given a confidence interval, find the difference of the upper bound and the error bound. If the error bound is unknown, then average the upper and lower bounds of the confidence interval to find the sample mean. Sometimes researchers know in advance that they want to estimate a population mean within a specific margin of error for a given level of confidence. In that case, solve the EBM formula for n to discover the size of the sample that is needed to achieve this goal: 2 2

PDF page 483: standard deviation is known. When estimating a population mean, the margin of error is called the error bound for a population mean (EBM). A confidence interval has the general form: (lower bound, upper bound) = (point estimate – EBM, point estimate + EBM) The calculation of EBM depends on the size of the sample and the level of confidence desired. The confidence level is the percent of all possible samples that can be expected to include the true population parameter. As the confidence level increases, the corresponding EBM increases as well. As the sample size increases, the EBM decreases. By the central limit theorem, σ EBM = z n Given a confidence interval, you can work backwards to find the error bound (EBM) or the sample mean. To find the error bound, find the difference of the upper bound of the interval and the mean. If you do not know the sample mean, you can find the error bound by calculating half the difference of the upper and lower bounds. To find the sample mean given a confidence interval, find the difference of the upper bound and the error bound. If the error bound is unknown, then average the upper and lower bounds of the confidence interval to find the sample mean. Sometimes researchers know in advance that they want to estimate a population mean within a specific margin of error for a given level of confidence. In that case, solve the EBM formula for n to discover the size of the sample that is needed to achieve this goal: 2 2

PDF page 484: α σ Standard Deviation is Known EBM = z ⋅ 2 n ̄ ̄ The confidence interval has the format ( x − EBM, x + EBM).

PDF page 482: 8.1 A Single Population Mean using the Normal Distribution In this module, we learned how to calculate the confidence interval for a single population mean where the population

PDF page 484: 8.1 A Single Population Mean using the Normal Distribution ̄ ⎛ σ ⎞ X ~N μ , The distribution of sample means is ⎝ X n⎠ normally distributed with mean equal to the population mean and standard deviation given by the population standard deviation divided by the square root of the sample size. The general form for a confidence interval for a single population mean, known standard deviation, normal distribution is given by (lower bound, upper bound) = (point estimate – EBM, point estimate + EBM) ̄ ̄ = ( x − EBM, x + EBM)

PDF page 484: EBM size (n) needed to achieve a desired margin of error at a given level of confidence General form of a confidence interval (lower value, upper value) = (point estimate−error bound, point estimate + error bound) To find the error bound when you know the confidence interval error bound = upper value−point estimate OR error bound upper value − lower value = 2 Single Population Mean, Known Standard Deviation, Normal Distribution Use the Normal Distribution for Means, Population