Statistics for AI and CS: Hypothesis Testing Assignment, Exercises of Statistics

Download Statistics for AI and CS: Hypothesis Testing Assignment and more Exercises Statistics in PDF only on Docsity! Statistics For AI and CS Hypothesis Testing Assignment 1 Awin Gray (s3073521) September 29, 2017 1 General Questions (a) A left-skewed distribution will have its median being greater than the mean because extreme observa- tions on the lower side will pull the average towards the low values. (b) P-value is the probability of observing the results as specified in the null hypothesis given that the null hypothesis is true. Type I error occurs when a researcher rejects the null hypothesis when the null hypothesis is true, thereby accepting a false positive. Type II error occurs when the researcher fails to reject a false null hypothesis, thereby accepting a false negative. These two conceptual types help distinguish between a null hypothesis and an alternative hypothesis. (c) 1. First, the research states the null and the alternative hypothesis 2. Decides on the level of significance 3. Collection of the data 4. Then chooses the test statistic to use and calculate the statistic 5. Construction of the rejection region 6. Based on the rejection region and the test statistic, one decides whether to reject the null hypothesis 2 Keeping body balance 1 Figure 1: box-and-whiskers plot (a) There is an outlier observed for the Elderly category while there is no outlier in the Young category as seen in Figure 1. The lower fence, the first quartile, the median, the third quartile and the upper fence for the elderly are all greater than the corresponding percentiles for the young individuals. (b) It is assumed that the data are normally distributed when constructing the confidence interval and that there are no extreme outliers. These assumptions seem to be tenable. The two populations from which the data is drawn have the same variance. It is also assumed that the observations are independent of each other. R-output: Welch Two Sample t-test data: sway$FBSway by sway$Age t = 2.3035, df = 10.971, p-value = 0.04183 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.3627401 16.0539266 sample estimates: mean in group Elderly mean in group Young 26.33333 18.12500 The 95% confidence interval for the difference in means is (0.3627, 16.0539). Observe that 0 is not included in the confidence interval. 2