Roger Amster teaches an English course in which 40 students are enrolled. After yesterdays class, roger questioned the 5 students who always sit in the back of the classroom. Three of the 5 said “yes” when asked if they would like a tale of two cities as the next class reading assignment.
a. Identify the population and the sample in this situation
b. Is this likely to be a representative sample? If not, why not?
2.5
The national center for health statistics reports the following age breakdown of deaths in the United States during 2002.
Age (years) number of deaths (thousands)
Under 15 40.01
15 – Under 25 33.08
25-under 35 41.38
35-under 45 91.01
45 under 55 172.21
55-under 65 253.73
65-under 75 424.11
75 or over 1391.99
Identify the following for the 45-under 55 classes:
(a) Frequency, (b) upper and lower limits, (c) width, and (d) midpoint
2.43
The following data represent x= the total number of businesses and y= the number of business failures in mountain states over a 1-year period.
x=number of y= number of
State Businesses business failures
Arizona 146,672 1090
Colorado 156,891 2091
Idaho 46,787 312
Montana 43,961 191
Nevada 38,593 255
New Mexico 55,334 319
Utah 58,156 372
Wyoming 26,383 178
a. Draw a scatter diagram representing these data.
b. Using the “eyeball” method, fit a straight line to the data.
c. Does there appear to be any relationship between the variables? If so, is the relationship direct or inverse?
We do not do your homework for you. However, I will give you a start.
If Roger did not assign the seating, what type of student would choose to sit in the back of the class (sample)? Would that type of student be representative of the whole class (population)?
An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling the appliances get damaged and must be sold at a reduced price. The company wishes to keep the proportion of damaged machines at 2%. It is believed, however, that this level is being exceeded at the warehouse. To investigate, an inspector randomly sampled 60 appliances ready for delivery and found 5 to be damaged. What is the parameter of interest?
a. In the first situation with Roger Amster's English course, the population would be all the students enrolled in the course (which is 40 in this case). The sample would be the 5 students who always sit in the back of the classroom that Roger questioned.
b. It is not likely to be a representative sample because the sample only includes 5 specific students who always sit in the back of the classroom. The opinions and preferences of these 5 students may not accurately reflect the opinions of the entire population of students enrolled in the course.
2.5 For the age breakdown of deaths in the United States in 2002, considering the 45-under 55 age class:
(a) Frequency: The frequency refers to the number of deaths in that particular age class, which is 172.21 according to the given data.
(b) Upper and lower limits: The lower limit for the 45-under 55 age class is 45, while the upper limit is 55.
(c) Width: The width is determined by subtracting the lower limit from the upper limit. In this case, the width is 55 - 45 = 10.
(d) Midpoint: The midpoint is calculated by taking the average of the upper and lower limits. In this case, the midpoint is (45 + 55) / 2 = 50.
2.43
(a) To draw a scatter diagram representing the data for the number of businesses and number of business failures in mountain states, you would plot the values as points on a graph. The x-axis would represent the number of businesses (x) and the y-axis would represent the number of business failures (y). Each state would have a corresponding point on the graph, with the x-coordinate representing the number of businesses and the y-coordinate representing the number of business failures.
(b) Using the "eyeball" method, you would visually approximate a straight line that best fits the data points on the scatter diagram.
(c) Based on the scatter diagram, if there is a relationship between the variables (number of businesses and number of business failures), it appears to be a direct relationship. This means that as the number of businesses increases, the number of business failures also tends to increase.