The distribution of marks are given below: Question # 1 2 3 4 5 6 Total Total Marks 3 6 6 4 6 4 29 Your Marks GOOD LUCK! 1 1. Calculate the mean and standard deviation of the following six numbers. [3 marks] 7 9 10 10 11 13 2. The following shows the amount of time, in minutes, that an individual spent doing cardio at the gym each day over a period of 14 days. Answer the following questions. [6 marks] 23 47 29 19 24 3O 0 33 23 20 37 27 20 33 a) Find the median and provide an interpretation of it. [2 marks] b) Use the interquartile range method to determine if there are any outliers? Briefly justify your work by showing your calculations. [4 marks] 3. An educator wanted to investigate if the amount of time spent on social media (measured in hours) had an effect on the academic performance (measured as GPA) of students. A random sample of 150 students was selected to investigate this. [6 marks] a) Identify the use of the two variables in this study. [1 mark] b) Suppose the sample correlation coefficient was found to be -O.362 (note it's negative). What conclusion can we say about all students in the population? Make sure you use the appropriate process to make the conclusion. [4 marks] c) Can we sayr "engaging in social media for longer periods of time is the cause of poor academic performance\"? Brieflyjustify your answer. [1 mark] 4. For each of the following situations, indicate the most appropriate (i) graphical display and (ii) statistic (i.e. numerical summary such as mean, quartiles, etc.) that we can use to summarize the following data. [4 ma rks] a) As part of campus safety audit, a sample of students and staff were asked how safe they feel when they walk to/from the bus stop or the parking lot. Their responses were ranked from 1 for 'very unsafe'r to 5 for 'very safe'. [2 marks] Graphical display: Statistic: b} From a sample of 150 customers, a bank records the number of minutes that each has to wait in a line-up. The distribution of time spent in a line-up is known to be rightskewed. [2 marks] Graphical display: Statistic: 5. To estimate the amount of stationary being "used\" by employees of a national company, the researcher first randomly selected 10 branches (among 100's of branches) across Canada and every employee in those branches was asked to report the amount of stationary they have used in the past 12 months. [6 marks] a) Identify the sampling method used above. Make sure you provide a detailed justication of your answer. [2marks] b) Does the above sample involve any sampling error? If so, brieflyjustify. If not, briefly explain why not. [2 marks] c) Does the above sample involve any response bias? If so, briefly justify. If not, briefly explain why not. [2 marks] 6. Many families on Vancouver Island are using backyard structures for home ofces, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized backyard structure is $3100 and that the standard deviation is $1200. Assume that the price distribution is a symmetric moundshaped or bell-shaped distribution. [4 marks] a) What is the z-score for a backyard structure costing $2300? Interpret this z-score [2 marks] b) lCan the price from part a) be considered an outlier? Justify your answer. [2 marks]