Illustrate Asymptotic Distribution of the OLS Estimator and t-Statistic?
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Illustrate Asymptotic Distribution of the OLS Estimator and t-Statistic?
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- Should we curve? For an exam with a maximum of 100 points, if the class's mean score is 80 and its standard deviation is 20, should we apply the normal curve to adjust grades and assign A to all students with a Z-score of 1 and above? Why or why not?Can we use the standard deviation to compare variability of two or more datasets? Is the z-score a real measure of dispersion? If the data is highly skewed, can we still rely on the kurtosis coefficient?Data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. According to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 1.6 standard deviations below the mean? What is the probability that the percent change in worker output from the previous quarter is between -1.56 and 4.33?
- The heart rate of 20 patients in the ICU have a mean of 95.3 beats per minute and a standard deviation of 19.6 beats per minute. Are heart rates from the ICU patients unusual given a normal heart rate has a mean of 72 beats per minute? What is the t-stastic?What would be the appropriate inferential statistic to evaluate the relationship between: • 'Generation' [Baby Boom (1946-1964), Generation X (1965-1980), Millennials (1981-1996)] • 'Household Income' (in US $) median and interquartile range means comparison (t or ANOVA) correlation coefficient (r) chi-square (x2) mean and standard deviation frequency and percentageScores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 8. The instructor wants to give an A to the students whose scores were in the top 08% of the class (Provide your answer with two decimal places). Find the Z-score that is associated with the lowest possible score to get an A. What is the minimum score needed to get an A?
- Biological oxygen demand (BOD) is a pollution index that is monitored in the treated effluent of paper mills. A certain paper mill has taken 31 samples over the past 3 months. The mean and standard deviation for the sample data are 3.42 and 0.728 ppm respectively. The mill would like to see if this sample indicates that the true average BOD in their treated effluent exceeds the targeted 3.00 ppm. Let ? = 0.05. A) The test statistic, (ttest), for this data set is: Note: Round your answer to the nearest hundredth.B) The p-value is: C) The statistical decision and corresponding English interpretation for this study are: Fail to reject Ha: conclude that the true BOD in treated effluent exceeds 3 ppmFail to reject Ho: we cannot conclude that the true BOD in treated effluent exceeds 3 ppm Reject Ha: we cannot conclude that the true BOD in treated effluent exceeds 3 ppmReject Ho: conclude that the true BOD in treated effluent exceeds 3 ppm1) Which is relatively better: a score of 88 on a Psychology test or a score of 45 on an Economics test? Scores on the Psychology test have a mean of 92 and a standard deviation of 10. Scores on the Economics test have a mean of 57 and a standard deviation of 5. Use measures of relative position to answer this exercise (Z-score).What raw score for age corresponds to a z- score of +4.50, given a mean of 12.0 years and a standard deviation of 4.0 years?
- Paramesan cheese is aged for an average of 24 months to allow it to develop the desire richness in flavor the standard deviation for the length of time Parmesan cheese is aged is 3.7 months How long would Parmesan cheese have to be aged in order to be in the 90th percentile? Assume that the data is normally distributedCalcium is essential to tree growth. In 1990, the concentration of calcium in precipitation in a certain area was 0.11milligrams per liter (mg/L).A random sample of 10 precipitation dates in 2018 results in the following data table. Complete parts (a) through (c) below. (B) With 98% confidence, the mean concentration of calcium in precipitation in this area in 2018 is betweenAssume that a population of thousands of people whose responses were used to develop the anxiety test had scores that were normally distributed with meand of 30 and standard deviation of 10. What proportion of people in this population would have anxiety scored within the following range of scores? between 10-50.
