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Chp 8-3 and 9 study

# Chp 8-3 and 9 study - CHP 8-3 Confidence interval for the...

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CHP 8-3 Confidence interval for the population mean (µ) is: (Std deviation) mean ('x-hat') ± n Must ask ourselves, “where did std deviation come from in the equation? - If it came from same sample as the mean, came from the t table ( s – sample stan dev.) - If it came from the Z table, it is the population standard deviation (σ) The sample mean, 'x bar', is the estimate of µ and is also called a point estimate , because it consists of a single number. Population mean – accuracy depends on sample size. We measure the precision of this estimate by constructing a confidence interval. When defining a confidence interval for µ, we can define 99%, 95%, 90% confidence interval, or whatever. The specific percentage represents the confidence level. The higher the confidence level, the wider the confidence interval. 8.4 If σ is unknown, it is impossible to determine a confidence interval for µ. This is no longer a standard normal random variable, Z. However, it does follow another identifiable distribution, the t distribution. Degrees of Freedom = df = n – 1 A more accurate confidence interval is always obtained using the t table when the sample standard deviation ( s ) is used in the construction of this interval. 8.5 Necessary sample size equation is: Must estimate std deviation A carefully chosen large sample generally provides a better representation of the population than does a smaller sample. To obtain a rough approximation of σ, you could ask a person familiar with the data to be collected two Qs: 1.) What do you think will be the highest value in the sample (H) or 2.) What will be the lowest value (L) H - L a rough approximation of σ is the anticipated range (H – L) divided by 4 so. .. σ = 4 If the pop stand dev (σ) is known, the stan normal table is used to derive the confidence interval. If σ is unknown, the t table is used to derive the confidence interval. For situations where is σ unknown and the sample size is greater than 30, approximate confidence intervals for the population mean can be constructed using the standard normal table. CHP 9

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Chp 8-3 and 9 study - CHP 8-3 Confidence interval for the...

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