Match each of the following vocabulary words or phrases with the correct definition or description. Confidence interval 2 Margin of error 3 Parameter 4 Hypothesis test 5 Statistic Match each of the options above to the items below. A numerical summary of a population A numerical summary of a sample The maximum amount by which the sample mean will differ from the true mean, with a given level of confidence A range of values on the number line, which we are confident contains the true mean A statistical tool for making a decision, based on data1. For each of the following statistical investigations, (1) suggest an appropriate graphical display for summarizing the data and (2) identify a statistic (numerical summary) that could be used to describe the data. [2 marks each] I a) A random sample of 150 customers of a retailers in Vancouver is obtained to study the relationship between the household income of the customer (less than $45,000, $45,000 to $89999, and over $90,000 or higher) and whether he or she has a store credit card (Yes or No). Graphical display: Statistic (numerical summary): b) The financial controller of a mid-size wholesaler wants to develop a statistical model to estimate the amount of time it takes to process invoices in his accounts receivable department. Data were collected from the past 30 days. For each day, the number of invoices processed and completion time (in minutes) were obtained. Graphical display:(12 points) Each year the EPA does an lysis on the current models of vehicles sold in EPA Estimated Annual Fuel Cost of 2017 Vehicles United States. The data provided in this example is a subset of this analysis, if you are curious you may access the full data set from the EPA website http:/www.fueleconomy.gov/feg/download.shtml. The following graphical display and numerical summary show the variable estimate annual fuel cost of new vehicles. i (1 points) What type of variable is annual fuel 500 1500 2000 2500 3000 3500 cost? Quantitative or Categorical? Cost in Dollars Sid Mean Min. Median 3" Q Max. Dev $1815 5459 $650 $1550 $1750 $2100 $3500 b. (4 points) Using the graphical display and numerical summary, thoroughly describe the distribution of estimated annual fuel cost. Include context, shape, center and spread of the data and whether there are any outliers. Match Feature First Quartile Maximum (non-outlier) Median Third Quartile Minimum (non-outlier)6.1.8) Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate crack in n = 10 cyclically loaded wing boxes reported the following crack lengths (in mm): 2.20, 2.98, 3.04, 1.78, 1.10, 1.29, 2.10, 2.50, 2.60, 2.55. Calculate the sample mean, sample standard deviation, prepare a dot diagram of the data and interpret the diagram and calculated sample statistics