Question 2: (20 marks) (a) The following are the data of heights (in cm) of a random sample of 9 males. 165.0 171.5 176.5 165.0 171.5 167.5 180.0 166.0 172.5 The data were entered into a computer and then the following results were generated. * ** Summary Statistics for height data * ** height Min: 165.00 let Qu. : 166.00 Mean : Median : ard Qu.: 172 .50 Max : 180.00 Total N: 9.00 Variance : Bed Dev. : 5.27 Sum: 1535.50 SE Mean: i. Calculate the four missing descriptive statistics, and write them in your answer booklet. [4 marks] ii. A graphical method was used to describe the data of heights of males (in cm) and the following graph was produced. What is the name of this type of graph? For this graph, comment on the distribution of the variable. 180 heights of males (in cm) 170 165(b) Assume that the height data in part (a) were taken from students at Charles Sturt University (CSU). i. Test at the 5% level of significance, to see if the data supports a null hypothesis that the average height of male students at CSU does not exceed 167.5 cm. State clearly the null and alternative hypotheses, the test statistic, test result and conclusion in terms of the original problem. You may use the following computer output. You may assume that the data meet the statistical assumptions necessary for the test to be appropriate. [6 marks] One Sample t-test data: height t = 1.7722, de = 8, p-value = 0.05715 alternative hypothesis: true mean is greater than 167.5 95 percent confidence interval: 167.3467 Inf sample estimates: mean of *: 170 . 6111 ii. Is this a one-tailed or a two-tailed hypothesis test? Justify your answer. [2 marks] (c) Suppose that you have a small disk, coloured white (W) on one side and black (B) on the other side. The disk is fair (i.e. the chance of getting black from a single flip is 509%). The disk is flipped three times. i. Complete the sample space (i.e. denoted by $) of this experiment below and write this in your answer booklet. 5 = {BBB, BBW, BWB, WBB, [1 mark] ii. For a random variable X = number of white sides from the three flips, complete the table below with appropriate values of the probability density function f(x), i.e. P(X=x) for each value of the random variable X. Write the table in your answer booklet. 2 3 f(x) 0.375 0.125 [2 marks] iii. Using the completed table find the probability of getting at least one white side. [2 marks]