STA 2023 Test 1 Review You may receive help at the Math Center.

Transcription

1 STA 2023 Test 1 Review You may receive help at the Math Center. These problems are intended to provide supplementary problems in preparation for test 1. This packet does not necessarily reflect the number, type, or topics of problems that will appear on the actual test, nor is it guaranteed to cover every topic that may appear on the test. Part I. Multiple Choice. Circle the letter of the best response. 1. A Johns Hopkins University researcher surveys all cardiac patients in each of 30 randomly selected hospitals. This is an example of (c) random sampling 2. A survey is conducted by stopping shoppers in the food court of Tallahassee Mall. This is an example of (a) random sampling 3. Households are classified according to race and income. From each category, 20 households are selected and asked to keep diary of their television viewing choices for one week. This is an example of 4. A door prize is given away at a home improvement show. Tickets are placed in a bin and the tickets are mixed up. Then a ticket is selected by a blindfolded person. This is an example of (d) random sampling 5. At airport security, passengers shoes are inspected for explosives. Every fifth passenger through the metal detector is selected for shoe inspection. This is an example of (b) random sampling 6. A survey of TCC students is taken, and it is reported that, based on the results of the survey, 47% of TCC students have a pet. If in fact the true proportion of TCC students who own a pet is 53%, this is an example of (a) Qualitative Error (b) Sampling Error (c) Systemic Error (d) Non-sampling Error

2 7. While compiling results of a study on household incomes, the data-entry clerk forgot to enter decimal points. This resulted in incomes being overstated by a factor of 100. This is an example of (a) Qualitative Error (b) Sampling Error (c) Systemic Error (d) Non-sampling Error 8. A study published in 1990 attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Twenty-three hundred Florida residents were surveyed. Which of the following is the population used in the study? (a) all Florida residents (b) the 2300 Florida residents surveyed (c) the Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters (d) all Florida residents who lived along the beaches 9. A local newspaper ran a survey asking Do you support the deployment of a weapon that could kill millions of innocent people? This is an example of (a) poorly defined frame (b) poorly worded question (c) rotated questions (d) sampling error 10. The 1995 payroll amounts for all mafor-league baseball teams are shown in the histogram. What percentage of the payrolls were in the $30-40 million range? 1995 Payroll of Baseball Teams (in millions of dollars) Number of Teams (a) 30.8% (b) 42.1% (c) 8% (d) 18.5% $0-10 $10-20 $20-30 $30-40 $40-50 Payroll

3 Part II 11. Categorize each of the following random variables as qualitative, continuous, or discrete. (Circle one choice for each) Time to failure of a computer hard drive qualitative continuous discrete Amount of an income tax refund qualitative continuous discrete Number of students taking statistics qualitative continuous discrete Colors of cars in the parking lot qualitative continuous discrete 12. The following information relates to the entire product line of BMW automobiles: (a) Identify the population. Body Weight Number Model Style (lbs) of seats M/Z3 Coupe Coupe M/Z3 Roadster Convertible Series Coupe Series Sedan Series Sedan Z8 Convertible (b) Identify the individuals. (c) Identify the variables and determine whether each variable is qualitative, continuous, or discrete

4 13. The graph below shows the price of light crude oil for January delivery, during trading on the New York Mercantile Exchange on November 26, The horizontal axis is the time of day; the vertical axis is the price. Explain why the graph is misleading. 14. A random sample of one thousand people was conducted, and respondents were asked the number of cups of coffee consumed per day. The pie chart shows the number of people who replied none, one, two, three, or four or more cups per day. Find the central angle of the sector for three cups of coffee per day. How Many Cups of Coffee Do You Drink on an Average Day? None 250 Four or more 289 One 125 Two 199 Three Find the mean, median, and mode of the following numbers:

5 For questions use the following data set. Enter the data into L 1 in your calculator. When you compute 1-Var Stats, you should see ΣX = Assume the data represent a population Report the mean using the appropriate symbol. 17. Report the mode. 18. Determine the range. 19. Report the population standard deviation, using the appropriate symbol. 20. Report the population variance, using the appropriate symbol. 21. Construct a frequency distribution for the data above, using a class width of 5. Let the lower class boundary of the first class be 20. Then construct a relative frequency distribution, cumulative frequency distribution, and cumulative relative frequency distribution. Relative Cumulative Cumulative Class Frequency frequency frequency rel. freq.

6 22. Construct a stem-and-leaf plot of the data. 23. At a tennis tournament a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 102 miles per hour (mph) and the standard deviation of the serve speeds was 9 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least three-fourths of the player s serves. 24. The average year old man is 69.9 inches tall, with a standard deviation of 3.0 inches, while the average year old woman is 64.6 inches tall, with a standard deviation of 2.8 inches. If the heights of men and women are normally distributed, give an interval that would contain the heights of approximately 95% of year old men.

7 Formula Page µ = Σ x N Σ (xi µ) σ = 2 N x = Σ x n Σ (xi x) s = 2 n 1