Point Estimation PDF

 Estimation refers to the process by which one makes inferences about a population, based on information obtained from a sample. * is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning and meta-analysis to plan experiments, analyse data a...

 Estimation refers to the process by which one makes inferences about a population, based on information obtained from a sample. * is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning and meta-analysis to plan experiments, analyse data and interpret results  Statisticians use sample statistics to estimate population parameters. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions. Point estimate Interval estimate  A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.  If the sample is not representative of the population being studied, the sample statistic may be biased so you cannot use it to make valid inferences about the population parameter To minimise bias the sample should be chosen by random sampling from a list of all individuals in the relevant population. This list is called the sampling frame. It is essential. For a simple random sample the individuals are chosen in such a way that each individual in the sampling frame has an equal chance of being selected. This may involve using computer generated random numbers to select the sample.  Estimates have low bias because their average is near the population parameter, but have high variability because they are widely spread and a single sample value could be far from the parameter. Estimates have bias because the expected value is not equal to the parameter. They also have high variability because they are widely spread out.  In this case the estimates are biased because all of them are systematically higher than the population parameter The sample statistics have, however, low variability because they are all close together. In this case the estimates have both low bias and low variability. Experimental design aims to simultaneously reduce bias and variability by producing a sampling distribution as shown.  As an example of a point estimate, assume you wanted to estimate the mean time it takes 12-year-olds to run 100 yards. The mean running time of a random sample of 12-year-olds would be an estimate of the mean running time for all 12-year- olds. Thus, the sample mean, M, would be a point estimate of the population mean, μ.  Roulette is a game of chance that originated in France in the eighteenth century. The roulette wheel is spun, and a small white ball is dropped into the wheel. When the wheel stops, the ball lands on a number between 0 and 36, inclusive. The numbers from 1 to 36 are red or black, and 0 is green. In 500 spins of a roulette wheel, the ball landed on red 230 times. Use the data to estimate the probability that the ball will land on red on the next spin. Express your answer as a decimal rounded to the nearest hundredth.  The probability of selecting a jack card from a deck of 52 cards is 1/13. If one card is selected at random from each of 600 decks, approximately how many jacks can we reasonably expect to draw? Round your answer to the nearest whole number.  The "Wheel of Luck" game is a popular attraction at the Altadena Spring Fair. After 500 spins of the wheel, the results are shown in the table below. Based on the data, estimate the probability that the wheel will land on yellow on the next spin. Express your answer as a decimal rounded to the nearest hundredth. Red Green Blue Purple Yellow 155 92 78 85 90