Question

From a sample of 500 items, 30 were found to be defective. the point estimate of the population proportion defective will be

Answer 1

Simple random samplingA method of selecting a sample in such a way that each item or person in the population being studied has the same likelihood of being included in the sample.Systematic SamplingSelecting every nth member from a populationSampling ErrorThe difference between a sample statistic and its corresponding population parameter.

-Sample Error of the mean=Sample mean-Population meanSampling DistributionA probability distribution of all possible sample statistics computed from a set of equal-sized samples that were randomly drawn from the same population
-Think of it as the probability distribution of a statistic from many samplesStratified Random SamplingUses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics
-Subgroup=stratum
-The size of the samples from each stratum is based on the size of the stratum relative to the populationTime-Series DataObservations taken over a period of time at specific and equally spaced time intervals.Cross-Sectional DataA sample of observations taken at a single point in time.Longitudinal DataObservations over time over multiple characteristics of the same entity
-For Example: Time-Series and cross-sectional data can be pooled in the same data setPanel DataContain observations over time of the same characteristic for multiple entities, such as debt/equity ratios for 20 companies over the most recent 24 quartersCentral Limit TheoremStates that for simple random samples of size n from a population with a mean and finite variance, the sampling distribution of the sample mean approaches a normal probability distribution with mean and a variance equal to (sig)^2/n as the sample size become large
-Useful b/c the normal distribution is relatively easy to apply to hypothesis testing and to the construction of confidence intervals.
-Specific inferences about the population mean can be made from the sample mean, regardless of the population's distribution, as long as the sample size is "sufficiently large" which usually mean (n is greater than or equal to 30)Important properties of the Central Limit Theorem-If the sample size is greater than or equal to 30 the sampling distribution of the sample means will be approximately normal.
-The mean of the population and the mean of the distribution of all possible sample means are equal
-The variance of the distribution of the sample means is (sig)^2/n=the population variance divided by the sample sizeStandard error of the sample meanThe standard deviation of the distribution of the sample means.
-When the standard deviation of the population is known, the standard error of the sample mean is calculated as (sigma)/SQRT(n)
-As the Sample size increases, the sample mean gets closer, on average, to the true mean of the population.Desirable Properties of an estimatorUnbiasedness, efficiency,consistencyUnbiased EstimatorThe expected value of the estimator is equal to the parameter you are trying to estimate. For example, because the expected value of the sample mean is equal to the population mean, the sample mean is an unbiased estimator of the population mean.Efficient EstimatorThe variance of its sampling distribution is smaller than all the other unbiased estimators of the parameter you are trying to estimate. the sample mean, is an unbiased and efficient estimator of the population mean