Section 1
Describing Central Tendency
Explain the difference between each of the following:a A population parameter and its point estimate.b A population mean and a corresponding sample mean.
Explain how the population mean, median, and mode compare when the population's relative frequency curve isa Symmetrical.b. Skewed with a tail to the left.c Skewed with a tail to the right.
Calculate the mean, median, and mode of each of the following populations of numbers:a 9,8,10,10,12,6,11,10,12,8b 110,120,70,90,90,100,80,130,140
Calculate the mean, median, and mode for each of the following populations of numbers:a 17,23,19,20,25,18,22,15,21,20b 505,497,501,500,507,510,501
Recall that Table 1.8 (page 20 ) presents the satisfaction ratings for the XYZ-Box game system that have been given by 65 randomly selected purchasers. Figures 3.8 and $3.11(a)-$ see page $144-$ give the Minitab and Excel outputs of statistics describing the 65 satisfaction ratings.a. Find the sample mean on the outputs. Does the sample mean provide some evidence that the mean of the population of all possible customer satisfaction ratings for the XYZ-Box is at least $42 ?$ (Recall that a "very satisfied" customer gives a rating that is at least $42 .$ ) Explain your answer.b. Find the sample median on the outputs. How do the mean and median compare? What does the histogram in Figure 2.15 (page 72 ) tell you about why they compare this way?
Recall that Table 1.9 (page 21 ) presents the waiting times for teller service during peak business hours of 100 randomly selected bank customers. Figures 3.9 and $3.11(\mathrm{~b})-$ see page $144-$ give the Minitab and Excel outputs of statistics describing the 100 waiting times.a. Find the sample mean on the outputs. Does the sample mean provide some evidence that the mean of the population of all possible customer waiting times during peak business hours is less than six minutes (as is desired by the bank manager)? Explain your answer.b. Find the sample median on the outputs. How do the mean and median compare? What does the histogram in Figure 2.16 (page 73 ) tell you about why they compare this way?
Consider the trash bag problem. Suppose that an independent laboratory has tested 30 -gallon trash bags and has found that none of the 30 -gallon bags currently on the market has a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30 -gallon bag will be the strongest such bag on the market if the new trash bag's mean breaking strength can be shown to be at least 50 pounds. Recall that Table 1.10 (page 21 ) presents the breaking strengths of 40 trash bags of the new type that were selected during a 40 -hour pilot production run. Figures 3.10 and $3.12-$ see page $144-$ give the Minitab and Excel outputs of statistics describing the 40 breaking strengths.a. Find the sample mean on the outputs. Does the sample mean provide some evidence that the mean of the population of all possible trash bag breaking strengths is at least 50 pounds? Explain your answer.b. Find the sample median on the outputs. How do the mean and median compare? What does the histogram in Figure 2.17 (page 73 ) tell you about why they compare this way?
Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, $350,45,$ $35,25,$ and $40 .$ Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"- the mean or the median? Explain.
Construct a histogram and a stem-and-leaf display of the teams' revenues.
Compute the mean team revenue and the median team revenue, and explain the difference between the values of these statistics.
Construct a histogram and a stem-and-leaf display of the teams' player expenses.
Compute the mean team player expense and the median team player expense and explain the difference between the values of these statistics.
Construct a histogram and a stem-and-leaf display of the teams' operating incomes.
The mean team operating income is the operating income each NBA team would receive if the NBA owners divided the total of their operating incomes equally among the 30 NBA teams. (Of course, some of the owners might object to dividing their operating incomes equally among the teams).a. How would the players use the mean team operating income to justify their position opposing a hard salary cap?b. Use Table 3.2 to find the number of NBA teams that made money (that is, had a positive operating income) and the number of teams that lost money (had a negative operating income).c. How would the owners use the results of part (b) and the median team operating income to justify their desire for a hard salary cap?