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(3) [H] (30 points) Determine whether each of the following 15 statements is true or false (write T or F beside each statement). If the statement is incorrect (F) correct the state- ment. For these questions, you do not need to show your detailed work. (a). A hypothesis test is performed and a p-value of 0.043 is reported. In this case, and using significance testing, the smallest a at which the null Inypothesis would be rejected is 0.0413. (b). Consider a confidence interval for a population mean. If the sample size n is doubled, then the width of the interval is halved. (c). A hypothesis test was conducted and the p-value was less than the significance level. It is known that the alternative hypothesis is true. This suggests that a type II error occurred. OH. Jankowski (d). A random sample of size n = 10 is drawn from a population with mean / and standard deviation o. Then the sample average X" has an approximately normal distribution with mean / and standard deviation o/ vn by the central limit theorem. (e). For any two events A and B, P(An B) = P(A)P(BIA). (f). The relative frequency for each class in a frequency distribution is a sample propor- tion. (g). Inferential statistics are used to draw a conclusion about a population. (h). In an equally likely outcome experiment, the probability of any event A is the number of outcomes in A. (i). In a two-sample paired & test, the before and after sample sizes must be the same. (). You are shown the following normal probability plot where the data set percentiles are on the y-axis. The sample size is n = 1, 000. The data set can best be described as skewed to the left. (k). For a data set with a strongly left-skewed histogram, the sample mean will be larger than the sample median. (1). Consider two events, A and B. The probability of event A is 0.55 and the probability of event B is 0.6. It follows that the events A and B cannot be disjoint. (m). The current median income per household in Toronto is about $78,000 annually. It is possible to alter the incomes of 85% of the population of Toronto and not change the median. (n). A data set is observed and a 95% confidence interval for the population mean is calculated to be (-0.3, 0.9). This means that the probability that the population mean / lies in (-0.3, 0.9) is 95%. (o). In a test of a statistical hypothesis, we attempt to find evidence in favour of the null hypothesis