Suppose that you want to estimate the number of miles driven per year among all drivers living in Vermont and how the number of miles driven is related to a driver’s age. Suppose that you obtain a list of all drivers licensed by the State of Vermont, then take a simple random sample of 1000 drivers from the list and ask them to complete a survey regarding their driving habits during the last year and their age. A total of 620 people complete the survey.

1. Identify the population, sampling frame, sample, and sample size.
2. List two ways that sampling bias may have been introduced.
3. Would you consider this to be a cross-sectional study or a longitudinal study? Explain your reasoning.

1. Consider the following set of data relating Distance from School and Time to get to school:

1. Construct a scatter plot for the given data.

2. Does the scatter plot show positive/negative/no correlation? Justify your answer.

3. Find the least-square regression line (Best fit line).

4. If a student lives 6.8 miles away from school, what is her predicted time to get to school?

1

e. Is there a linear correlation between the two variables? (Hint: find t-test statistic value)

The file Sedans contains the overall miles per gallon
(MPG) of 2013 midsized sedans:
38 26 30 26 25 27 22 27 39 24 24 26 25
23 25 26 31 26 37 22 29 25 33 21 21
Source: Data extracted from “Ratings,” Consumer Reports, April
2013, pp. 30–31.
a. Compute the mean, median, and mode.
b. Compute the variance, standard deviation, range, coefficient of
variation, and Z scores.
c. Are the data skewed? If so, how?
d. Compare the results of (a) through (c) to those of Problem 3.12
(a) through (c) that refer to the miles per gallon of small SUVs.

tire manufacturer claims that the life span of its tires is 60,000 miles. Assume the life spans of the tire are normally distributed. You selected 25 tires at random and tested them. The mean life span of the sample is 58,800 miles. The tires had a sample standard deviation, s = 600. Use the .10 level of significance.

1. 1. Which distribution would be indicated?
   2. Explain why you chose that distribution.
   3. Construct a confidence interval for the mean using the above data. Use the .10 level of significance.
   4. Re-compute the confidence interval if “n” is increased to 125 with the same mean and standard deviation.
   5. Re-compute the confidence interval if level of significance .01 with the same mean and standard deviation with the original n.

The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How far does the object travel horizontally before it hits the water?

102 m

118 m

137 m

155 m

173 m

The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How fast is it going when it hits the water?

79.3 m/s

33.5 m/s

50.7 m/s

57.4 m/s

60.7 m/s

Each of the five (5) workers in a factory is being paid $250 per day. For every unit produced in excess of 25 units in one day, a worker is paid $12. Fixed factory overhead per annum is $198,000 and there are approximately 330 working days in one year. Production data for July 6 and 7, 20C show the following number of units produced by each worker: July 6 = Cass - 25, Jen - 27, Owen - 24, Henry - 24, Miles - 28; July 7 = Cass - 26, Jen - 26, Owen - 28, Henry - 27, Miles - 26. What is the average direct labor cost per unit for the two-day period?

City Mileage, Highway Mileage. We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's 2013 Fuel Economy Guide give the regression line

highway mpg = 6.785 + (1.033 x city mpg)

for predicting highway mileage from city mileage.

(a) What is the slope of this line? Say in words what the numerical value of the slope tells you.

(b) What is the intercept? Explain why the value of the intercept is not statistically meaningful.

(c) Find the predicted highway mileage for a car that gets 16 miles per gallon in the city. Do the same for a car with city mileage of 28 mpg.

Use your calculator to determine the probabilities. State what you put in for the lower limit, upper limit, mean and standard deviation.

1. Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.5 inches. Find the percentage of trees having a diameter greater than 17 inches

2.White blood cell (WBC) count per cubic millimeter of whole blood follows approximately a Normal distribution with mean 7500 and standard deviation 1750. What percentage of people have WBC between 7500 and 8500?

3. Lifetimes of a certain brand of tires is approximately normally distributed with mean 40,500 miles and standard deviation 3,500 miles. What percentage of tires will last more than 50,000 miles?

4. The incomes of a set of factory workers happen to be normally distributed. The average income is $53,000 and the standard deviation is $5,000

1. What is the probability that a randomly selected employee makes more than $55,000?
2. What is the probability that the average of 4 randomly selected employees makes more than $55,000
3. What is the probability that the average of 12 randomly selected employees makes more than $55,000?

1. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability. To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference?