(a) salary of a bank executive (measured in dollars) quantitative. (c) SAT scores of students at Millersville University quantitative

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1 Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Test 1 February 8, 2010, 10:00AM-10:50AM Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of statistical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. (2 points each) Consider the types of variables in the list below. Label each variable as to whether it is a qualitative or quantitative variable. (a) salary of a bank executive (measured in dollars) quantitative (b) gender of a bank executive qualitative (c) SAT scores of students at Millersville University quantitative (d) preferred soft drink flavor (lemon-lime, cherry, cola, etc.) qualitative (e) marital status of a bank executive qualitative

2 2. (2 points each) For each of the following quantitative variables, indicate whether each is a discrete or continuous variable. (a) Number of children in a family. discrete (cannot have a fractional number of children) (b) Amount of income tax paid in continuous (can pay a fraction of a dollar in tax) (c) Height of a student in MATH 130. continuous (d) Yearly amount of snowfall in Millersville, PA. continuous (e) Number of cars parked at Disney World. discrete (cannot have a fraction of a car parked) 3. (5 points) The data below show the number of times a sample of 30 automatic teller machines (ATM) were used yesterday. Construct a stem-and-leaf plot of the data. How does the distribution of the data appear to be shaped? Stem Leaves The data could be described as skewed left.

3 4. (2 points each) Determine the type of sampling (random, stratified, cluster, convenience) being conducted in the following situations. (a) The 400 largest companies in the US are divided into 5 subsets according to the percent of revenue spent on advertising. Ten companies within each subset are randomly selected for a marketing study. stratified (b) A library conducts a user satisfaction survey by giving questionnaires to people who approach the library reference desk. convenience (c) The leasing manager of a mall assigns a number to each store in the mall and then randomly selects 8 numbers and reviews the lease of the corresponding store. random (d) The PA Department of Environmental Protection divides the state into 20 geographical regions, randomly selects one region, and audits all the industrial facilities in that region. cluster

4 5. (4 points each) A pizza company wants to introduce a new flavor of sausage topping for their pizza. They conduct a study in which ten people give a rating to the taste of the new pizza. The ratings are in the table below Determine each of the following measures of the sample. (a) x x = X n = = 33.1 (b) M If the data are arranged in ascending order then we have the following Since n = 10 is even then M = = (c) mode mode = 34 (d) midrange midrange = minimum + maximum 2 = = 30.0 (e) range range = maximum minimum = = 32 (f) s 2

5 X X x (X x) s 2 = (X x) 2 n 1 = = The alternative formula also gives the same result. X X X = 331 X 2 = s 2 = X 2 ( X) 2 n 1 n = (331) = = 121.0

6 6. (4 points each) For a collection of 20 samples of blood taken from cats, the mean concentration of hemoglobin (measured in g/dl) was and the standard deviation was (a) Calculate the z-score corresponding to a hemoglobin concentration of 11.2 g/dl. z = X x s = = 0.59 (b) Calculate the hemoglobin concentration corresponding to a z-score of 1.5. X = (z)(s) + x = ( 1.5)(1.89) = g/dl

7 7. (4 points each) The LTP Pipe Company manufactures plastic pipe for plumbing applications. The quality control department measured a sample of pipes being bundled for delivery to a customer. The mean diameter of the pipes was 3.5 inches with a standard deviation of 0.17 inches. (a) If the data in the sample follow a bell-shaped distribution, then 68% of pipe diameters will measure between 3.33 and 3.67 inches. According to the Empirical Rule 68% of normally distributed data fall within one standard deviation of the mean. µ σ = = 3.33 µ + σ = = 3.67 (b) If the data in the sample follow a bell-shaped distribution, then 95 % of the pipe diameters will be between 3.16 and 3.84 inches. Note that µ 2σ = 3.5 (2)(0.17) = 3.16 µ + 2σ = (2)(0.17) = 3.84, the given diameters are two standard deviations away from the mean. (c) LTP Pipe Company will allow a customer to return as defective any pipe that has a diameter of less than 3.16 inches. What percentage of pipes can the company expect to have returned? Assume the distribution of pipe diameters is bell-shaped. According to the Empirical Rule only 2.5% of the pipes can be expected to be returned because they have a diameter of less than 3.16 inches.

8 8. (3 points each) The data in the following table represents the number of days customers take to pay their electric bills. (a) Find the 1st quartile Q Thus Q 1 = P 25 = ( )/2 = i = 25 (30 + 1) = (b) Find the 75th percentile P 75. Thus Q 3 = P 75 = ( )/2 = i = 75 (30 + 1) = (c) What is the percentile rank of 45? k = # less than 45 n 100 = = (d) Find the interquartile range. IQR = Q 3 Q 1 = = 18 (e) Find the lower and upper fences for the sample. lower fence = Q 1 (1.5)(IQR) = 32.5 (1.5)(18) = 5.5 upper fence = Q 3 + (1.5)(IQR) = (1.5)(18) = 77.5 (f) Does the sample contain any outliers? If so, list them. Since X = 92 is above the upper fence, it is an outlier.