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1. lefttopFind the minimum, maximum, quartiles and median, sketch two side-by-side box plots to compare the speed of northbound and southbound cars on this isolated stretch of highway. How would you compare the speeds between the Northbound and Southbound cars? Be sure you discuss differences/similarities in shape, center and spread.Is the median or mean a more appropriate choice for describing the “centers” of these two distributions? Discuss any influence of outliers if applicable.2.3.The histogram below shows the distribution of heights (to the nearest inch) of 1,000 young women.What is the width of each bar? What does the height of the bar represent?The mean of the distribution of women’s heights is 64.6 inches, and the standard deviation is 2.75 inches. Interpret the mean and standard deviation in this context.Mark the mean on the graph, and mark one deviation above and below the mean. Approximately what proportion of the values in this data set are within one standard deviation of the mean? Draw a smooth curve that comes reasonably close to passing through the midpoints of the tops of the bars in the histogram. Describe the shape of the distribution.Shade the area under the curve that represents the proportion of the data within one standard deviation of the mean.4.Suppose that SAT mathematics scores for a particular year are approximately normally distributed with a mean of 510 and a standard deviation of 100.What is the probability that a randomly selected score is greater than 610?Greater than 710?Between 410 and 710?5. Jane wants to sell her Subaru Forester, but doesn’t know what the listing price should be. She checks on and finds 22 Subarus listed. The table below shows age (in years), mileage (in miles), and listed price (in dollars) for these 22 Subarus. (Collected on June 6th, 2012 for the San Francisco Bay Area.)Make appropriate plots with well-labeled axes that would allow you to see if there is a relationship between price and age and between price and mileage. Describe the direction, strength and form of the relationships that you observe. Does either mileage or age seem to be a good predictor of price?If appropriate, describe the strength of each relationship using the correlation coefficient. Do the values of the correlation coefficients agree with what you see in the plots?Pick the stronger relationship and use the data to find an equation that describes this relationship. Make a residual plot and determine if the model you chose is a good one. Write a few sentences explaining why (or why not) the model you chose is appropriate.If Jane’s car is 9 years old with 95000 miles on it, what listing price would you suggest? Explain how you arrived at this price.6. A student interested in comparing the effect of different types of music on short-term memory conducted the following study: 80 volunteers were randomly assigned to one of two groups. The first group was given five minutes to memorize a list of words while listening to rap music. The second group was given the same task while listening to classical music. The number of words correctly recalled by each individual was then measured, and the results for the two groups were compared.Is this an experiment or an observational study? Justify your answer. In the context of this study, explain why it is important that the subjects were randomly assigned to the two experimental groups (rap music and classical music). 7. In a study of college freshmen, researchers found that students who watched TV for an hour or more on weeknights were significantly more likely to have high blood pressure, compared to those students who watched less than an hour of TV on weeknights. Does this mean that watching more TV raises one’s blood pressure? Explain your reasoning.8.1. Find the estimated margin of error when estimating the proportion of red chips in a mystery bag if 18 red chips were drawn from the bag in a random sample of 50 chips. Explain what your answer to Problem 1 tells you about the number of red chips in the mystery bag in terms of where your sample proportion is with respect to your population proportion. How could you decrease your margin of error? Explain why this works. ................
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