Practice question (Part 2) solutions for midterm 1

Practice Question for Midterm 1 1 Population parameters are difficult to calculate due to A. cost prohibitions on data collection. B. the infeasibility of collecting data on the entire population. C. the fact that samples are difficult to draw due to the nature of the data. D. both cost prohibitions on data collection and the infeasibility of collecting data on the entire population. 2 The Fahrenheit scale for measuring temperature would be classified as a(n) A. ratio scale. B. ordinal scale. C. interval scale. D. nominal scale. 3 The following data represent a sample of property sales in Cape May County during the year 2000. Identify the qualitative and quantitative variables. What are the natural categories for Town and Class? Identify the measurement scales for all variables. Variables in town and class are qualitative variables. Variables in date, price, and assessment are quantitative. Town – Nominal. Class – Nominal. Date – Ordinal. Price – Ratio, Assessment - Ratio 4 The following is a list of five of the world's busiest airports by passenger traffic for 2010.

Name Location # of Passengers (in millions) Hartsfield-Jackson Atlanta, Georgia, United States 89 Capital International Beijing, China 74 London Heathrow London, United Kingdom 67 O’Hare Chicago, Illinois, United States 66 Tokyo Tokyo, Japan 64 How many more millions of passengers flew out of Atlanta than flew out of Chicago? A. 13 B. 21 C. 23 D. 25 89-66=23 5 The following data represent the recent sales price (in $1,000s) of 24 homes in a Midwestern city. 187 125 165 170 230 139 195 229 239 135 188 210 228 172 127 139 122 181 196 237 115 199 170 239 Suppose the data are grouped into five classes, and one of them will be "165 up to 190." -that is, {x; 165 ≤ x < 190}. The frequency of this class is _____. A. 6/24 B. 7/24 C. 6 D. 7 Frequency is counting, and relative frequency is proportion. Count the number of values that fall into the range from 165 to 190 (165 is included, but 190 is not included) = 7 6 Each month the Bureau of Labor Statistics reports the number of people (in thousands) employed in the United States by age. The accompanying frequency distribution shows the results for August 2011. Age Frequency Relative Frequency Cumulative Relative Frequency 16 to 19 4,794 4794/140335 4794/140335 20 to 24 13,273 13273/140335 (4794+13273)/140335 25 to 34 30,789 30789/140335 (4794+13273+30789)/140335 35 to 44 30,021 30021/140335 (4794+13273+30789+30021)/140335 45 to 54 32,798 32798/140335 (4794+13273+30789+30021+32798)/14033 5 55 and over 28,660 28660/140335 (4794+13273+30789+30021+32798+28660 )/140335 a. Construct a relative frequency distribution. What proportion of workers is between 20 and 24 years old? Total frequency: 140335. Relative frequency is a proportion. So, the proportion of workers between 20 and 24 years old is 13273/140335 = 0.0945. Likewise, try constructing relative frequency distribution for all the age group. b. Construct a cumulative relative frequency distribution. What proportion of workers is younger than 35 years old? (4794+13273+30789)/140335 = 0.3481 c. Construct a relative frequency histogram. Try constructing one. 7.

Variance of the number of visitors= [(26-35)2+(18-35)2+(14-35)2+(22-35)2+(55-35)2+(75-35)2]/(6-1) = 596 Standard deviation of the number of visitors: 24.413 Using the same method, Variance of revenue=5.052 Standard deviation of revenue = 2.24 b. There is no linear relationship as we cannot say the direction (increase or decrease) of one variable from another. 11. The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday’s Business Statistics exam. 3 12 2 3 5 The mean and the median of the numbers of hours spent by the five students are _______________. A. 2 hours and 5 hours, respectively B. 3 hours and 5 hours, respectively C. 5 hours and 2 hours, respectively D. 5 hours and 3 hours, respectively In an ascending order, we have 2, 3, 3, 5, 12 Mean = 5, Median=3, D. 12. The Yearly Prices (rounded to the nearest dollar) for GLD (a gold exchange traded fund) and SLV (a silver exchange traded fund) are reported in the following table. Year GLD SLV Jan-08 $83 $15 Jan-09 $87 $11 Jan-10 $110 $17 Jan-11 $139 $30 Calculate the sample variance and sample standard deviation for the GLD ETF and SLV ETF. Which asset had a greater variance? Mean of GLD = 104.75 Mean of SLV = 18.25 Variance of GLD = [(83-104.75) 2 +(87-104.75) 2 +(110-104.75) 2 +(139-104.75) 2 ]/(4-1)= 662.96 Standard deviation of GLD = 25.74 Using the same method, Variance of SLV = 67.58 Standard deviation of SLV=8.22 Therefore, GLD has greater variance. 13. The following data represents the actual talk time, in hours, for the iPhone for 11 users. 25.1 19.1 21.6 9.5 20.3 18.0 24.6 25.2 21.9 29.7 28.5 What percentile is the talk time of 21.6 hours? A. 41st

B. 49th C. 54th D. 58th 21.6 hours is 5 th value in the ascending order of data distribution. Using Lp formula (6=12(p/100)), p=41.6. A. 14. The following sample data shows the starting salaries of seven graduates from the accounting program at California Polytechnic State University. The data are in thousands of dollars. 24 46 48 52 56 58 60 a. Calculate and interpret the 25th, 50th, and 75th percentiles. b. Are there any outliers? Is the distribution symmetric? If not, comment on its skewness. a. There are 7 data (n=7) L25=8(25/100) = 2 -> 46 L50=8(50/100) = 4 -> 52 L75=8(75/100) = 6 -> 58 b. 1.5IQR below Q1 or above 3. 24 is an outlier as 1.5IQR is 18, and 24 is 20 away from Q1 which is 46. Mean is 49.142, and median is 52. Median is greater than mean, which is the case of negatively skewed distribution. 15. Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following is a frequency distribution of speeds. The following frequency distribution represents the number of hours studied per week by a sample of 50 students. Speed (miles per hour) Frequency 45 up to 55 50 55 up to 65 325 65 up to 75 275 75 up to 85 25 The mean speed of the automobiles traveling on this road is the closest to ____. A. 55.0 B. 57.8 C. 64.1 D. 65.0 16. Sales for Adidas grew at a rate of 0.5196 in 2006, 0.0213 in 2007, 0.0485 in 2008, and –0.0387 in 2009. The average growth rate for Adidas during these four years is the closest to _______. A. 3.49% B. 11.83% C. 13.77% D. 14.02%