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I need examples that I can understand for these terms: point estimate, confidence interval, unbiased estimate, critical value, level of confidence, null hypothesis, type 1 error, hypothesis test, central region, and maximum error of error. Examples used in daily life. I am in the medical field. I think I could understand the terms better by examples and how it relates in health care. Term Point estimate Definition Example It is a single value that is used to estimate The sample mean bold sugar the population parameter. level x-bar is a point estimate of the population mean blood sugar level μ. Confidence Interval It is an interval which is used to express Suppose for a sample of 120 the degree of uncertainty associated with flies, the survival time has the a sample statistic. following data: It gives an estimated range of values n = 120, = 18.3 and = 5.2 which is likely to include an unknown The 95% C. I. for the mean population parameter, the estimated survival time is 17.369 days range being calculated from a given set of 19.231 days. sample data. Unbiased estimator Critical value(s) If the mean of the sampling distribution of The mean of the sample means a statistic is equal to a population is usually taken as an unbiased parameter, that statistic is said to be an estimate of the population unbiased estimator of the parameter. mean, since the two are equal The critical value(s) for a hypothesis test is The critical values for a two- a threshold to which the value of the test sided z- test for a population statistic in a sample is compared to mean heart rate, at 5% level of determine whether or not the null significance are -1.96 and +1.96 hypothesis is rejected. The critical value for any hypothesis test depends on the significance level at which the test is carried out, and whether the test is one-sided or two-sided. Level of confidence The confidence level is the probability Suppose an opinion poll value (1 – ) associated with a confidence predicted that, if elections were interval. It is often expressed as a held today, the party in power percentage. would win 70% of the vote. If the pollster attaches a 95% confidence level to the estimate, then it means that there is a 95% chance of the actual percentage falling between 68% and 72% Null hypothesis The claim made by the researcher with For example, if a quality control respect to a problem or issue in question inspector believes that the mean forms the Alternate hypothesis (Ha). The diameter of a population of opposite of this claim forms the Null syringes produced by a process hypothesis (H0). Thus, The null hypothesis is 12.00 mm, then Ha: = 12.00, is chosen to be the opposite of the claim, while H0 = ≠ 12.00. that is, opposite of what the researcher hopes or believes is true. Type I error Type I error (The False Positive) is the A student accused of copying in error of rejecting a true null hypothesis a medical examination when she really did not It is the process (usually in 5 steps) to Suppose 60 tosses of a coin gave determine whether to accept or reject a 38 Heads. We can formulate a null hypothesis, based on sample data. hypothesis as follows and do the testing to make out if the coin is Hypothesis test biased: H0: The coin is not biased, that is p = 0.5 Ha: The coin is biased, that is p ≠ 0.5 Critical region The critical region or the rejection region If the z- score for a sample is 2.1 is a set of values of the test statistic for then the null hypothesis that the which the null hypothesis is rejected in a mean of the population is less hypothesis test. than a stated value will be rejected at 95% level of significance because the critical z- score at this level is 1.96 Maximum error of estimate It is the greatest possible distance If standard deviation s = 6 and between the point estimate and the value the sample size, n = 25, at 95% of the parameter being estimated, at a confidence level, the maximum given confidence level error of estimate is E = z * s/n = 1.96 * 6/25 = 2.352.