Question

Selecting a random sample is an example of a statistical experiment, and the sample statistic p is a numerical description of the result of the experiment. Therefore, p is a random variable. The probability distribution of p is called the sampling distribution of p In practice, you select one random sample and use the information from that sample to estimate the population parameter of interest. However statisticians sometimes perform a procedure called repeated sampling, in which the experiment is run over and over again, and the value of the sample statistic from each run of the experiment is recorded. The distribution of the sample statistics from the repeated sampling is arn approximation of the sample statistic's sampling distribution Repeated sampling is used to develop an approximate sampling distribution for p when n 50 and the population from which you are sampling is binomial with p .20. Using Minitab, 1,000 random samples are drawn. The sample proportions for the 1,000 samples are located in the Proportions data set in the variable Sample Proportion. (The 15 samples in the Samples data set correspond to the first 15 sample proportions in the Proportions data set.) Data Set Proportions Sample Proportion Variable Sample Proportion Location Minimum Median Mean Maximum Full Data 0.04 0.2000 0.2021 0.38 Quartiles Full Data Sample Proportion Quantitative Observations 1000 Missing 0 Values1000 01 Median 03 0.1600 0.2000 0.2400 Variability & Shape Values Range Interquartile Range Standard Deviation Coefficient of Variation Skewness 1,000 0.34 0.0800 0.0552 27% 0.13 Deciles 10% 20% 30% 40% Median 60% 70% 80% 90% 0.1400 0.1600 0.1800 0.1800 0.2000 0.2200 0.2400 0.2400 0.2800 His Box Plots Filter: Include observations between... Maximumm Correlation Correlation If the sample you select for your statistical study is one of the 1,000 samples we drew in our repeated sampling, the worst-luck sample you could draw is proportion. Use the tool to sort the observed values of p from least to greatest. That is, in the Data Set section of the tool under Observations click the downward-pointing triangle directly below the Sample Proportion label. This will sort the sample proportions.) (Hint: The worst-luck sample is the sample whose sample proportion is farthest from the true population The mean of the approximation of the sampling distribution obtained from repeated The mean of the sampling distribution of p is sampling is The standard deviation of the sampling distribution of p is obtained from repeated sampling is The standard deviation of the approximation of the sampling distribution Consider the the approximation of the sampling distribution obtained from repeated sampling. Of the sample proportions one standard deviation of the mean deviations of the mean. [Hint: Use the tool to filter for the desired sample proportions. That is, under the filter section of the Statistics page for the variable Sample Proportion, enter the appropriate values for Minimum and Maximum in their respective entry fields. Applying the filter will then allow you to obtain the number of values (located directly across from the Values label) that lie within the specified range.] fall within fall within two standard deviations of the mean, and fall within three standard 160 140 Examine the frequency histogram for the the approximation of the sampling distribution obtained from repeated sampling shown at right. A normal curve is superimposed on the histogram. 120 100 80 60 40 20 Based on the histogram and your answers to the previous set of questions, the the approximation of the sampling distribution obtained from repeated sampling appears to be skewed to the right neither normal nor uniform approximately uniform approximately normal 0.02 0.08 0.14 0.20 0.26 0.32 0.38 Values of p-bar

Answer 1

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