Triola Assignment B
Section 4-2 – Basic Skills and Concepts
1) What does it mean when we say that “the probability of winning the grand prize is the Illinois lottery is 1/20358520? Is such a win unusual?
A parameter is value (number) that refers to the entire population being studied. A statistic is a value (number) that refers to a sample of a larger population.Check: OK
3) Determine whether the given value is a statistic or a parameter: A sample of households is selected and the average (mean) number of people per household is 2.58.
2.58 is a statistic because it the mean for a sample of the larger population.Check: OK
5) Determine whether the given values are from a discrete or continuous data set: In the Chapter Problem, it was noted that when 50 letters were sent as part of an experiment, three of them arrived at the target address.
The values are from a discrete set because it does not make sense in the context of the problem to have a decimal part of a letter.Check: OK
7) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
9) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
11) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
13) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
17) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
19) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
23) Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate: The years of cicada emergence: 1936, 1953, 1970, 1987, and 2004.
The years would be considered an interval measurement since it is possible to determine differences between the various years, but there is no zero level that represents zero time. Check: OK
Section 1-3 – Basic Skills and Concepts
1) What is a voluntary response sample, and why is it generally unsuitable for methods of statistics?
A voluntary response sample is a collection of participants who determine for themselves whether or not to participate in a study. Examples of voluntary response samples might include: individuals who respond to an Internet survey, individuals who respond to a mail-in survey, etc.
Voluntary response samples are not generally suitable because they lack the key characteristic of randomness. In addition, there is no guarantee that the participants that comprise the sample accurately reflect the composition of the larger population. In general, the results obtained from a voluntary response sample cannot be accurately generalized to the larger population. The population is likely to be biased.Check: OK after adding in phrase about bias.
5) Use critical thinking to develop an alternative conclusion: Based on a study of heights of men and women who play basketball, a researcher concludes that the exercise from playing basketball causes people to grow taller.
Based on the characteristics and requirements of the game of basketball, athletes who are taller generally tend to play basketball. Check: OK
17) An economist randomly selects 10 wage earners from each of the 50 states. For each state, he finds the average of the annual incomes, and he then adds those 50 values and divides by 50. Is the result likely to be a good estimate of the average (mean) of all wage earners in the United States? Why or why not?
The economist found the average of the 10 people in a state in order to determine the mean annual income for that. After determining the averages for each of the 50 states, he found the average of the averages in order to determine a mean for the entire country. Although his procedure was mathematically correct, the process has several flaws with regard to his sample.
First, the sample size is much too small to give an accurate reflection of the entire population. Even if he chose to find a single average of all 500 people, 500 is too small of a number to accurately represent a population of 300000000.
Second, each state has different characteristics with respect to population, socioeconomic status, job market, geography, and so forth. For example, California has a significantly higher population than Rhode Island. Thus, choosing 10 people from Rhode Island and 10 people from California does not accurately reflect the characteristics of the population.Check: OK
Section 1-4 – Basic Skills and Concepts
1) What is the difference between a random sample and a simple random sample?
A random sample is used when every individual in a population has an equal chance of being selected to be in the sample. For example, suppose that the population consists of every student in the school. If sample of 50 students is taken, every student in the school has an equal chance of being chosen. A simple random sample is when every possible sample of a given size has an equal chance of being selected. From the previous example, every possible combination of 50 students has an equal chance of being selected. It would not be simple random sample if the students were placed into permanent groups of 10 and 5 groups were randomly selected.Check: OK
5) Determine whether the given description corresponds to an observational study or an experiment: Nine-year-old Emily Rosa became an author of an article in the Journal of the American Medical Association after she tested professional touch therapists. Using a cardboard partition, she held her hand above the therapist’s hand, and the therapist was asked to identify the hand that Emily chose.
This would be considered an observational study since the participants are being observed but not changed by the procedure. Check: My original thought was that it was an experiment. I overlooked looked the condition that the participant or subject is treated (or modified) in an experiment. OK
9) Identify the type of observational study (cross-sectional, retrospective, prospective): A researcher from Mr. Sinai Hospital in New York City plans to obtain data by following (to the year 2015) siblings of victims who perished in the WorldTradeCenter terrorist attack of September 11, 2001.
This is an example of a prospective (or longitudinal) study since the research plans to follow the participants for an extend period of time and collect data at some point or points in the future.Check: OK
21) Identify which type of sampling is used: In a Gallop poll of 1059 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers there were called.
This is an example of random sampling since the phone numbers are randomly determined. Check: OK
Unit 1 – Review Exercises
1) Shortly after the WorldTradeCenter towers were destroyed by terrorists, American Online ran a poll of its Internet subscribers and asked this question: “Should the WTC towers be rebuilt?” Among the 1,304,240 responses, 768,731 answered yes, 386,756 answered no, and 248,753 said that is was too soon to decide. Given that this sample is extremely large, can the responses be considered to be representative of the population of the U.S.? Explain.
Due to the fact that sampling process involved voluntary response, it cannot be assumed that the sample is representative of the entire population. Most likely, people who had strong feelings about the response were the ones that responded. In addition, the poll was only available to those with Internet access.Check: OK
3) Identify the level of measurement used in each of the following?
a) The weight of people being hurled through the air…
Continuous RatioCheck: OK
b) A movie critic’s ratings of “must see, recommended, not recommended…”
Discrete OrdinalCheck: OK
c) A movie critic’s classification of “drama, comedy, adventure”
Discrete NominalCheck: OK
d) Bob, who is different in many ways, measures time in days, with 0 corresponding to his birth date…
Discrete IntervalCheck: OK
5) Identify the type of sampling used when a sample of the 366000 Coke shareholders is obtained as described. Then determine if the sample is representative of the population:
a) A complete list is compiled and every 500th name is selected
Systematic – This will be representative.Check: OK
b) At the annual stockholders’ meeting, a survey is conducted of all who attend
Convenience – The sample will be representative depending on the number of stockholders who attend. However, if only those who care the most about the meeting attend, then the sample may not be representative.Check: OK
c) Fifty different stockbrokers are randomly selected, and a survey is made of their clients…
Stratified – This will not be representative because different stockbrokers may have different numbers of clients.Check: The answer is clustered since stockholders are grouped by stockbroker and then sampled. The sample is not representative.
d) A computer file of all stockholders is compiled and numbered and a computer generates random numbers to select the sample…
Random – This will be representative. Check: OK
e) All of the stockholder zip codes are collected and 5 stockholders are randomly selected from each zip code
Clustered – This will not be representative since there may a larger concentration of stockholders in one zip code versus another (i.e. urban areas versus rural areas).Check: The sampling is stratified since the stockholders are grouped by zip code and then randomly sampled. The sample is not representative.
Unit 1 – Cumulative Review Exercises
1)Sum = 3.0630 + 3.0487 + 2.9149 + 3.1358 + 2.9753 = 15.1377Check: OK
Mean = 15.1377 ÷ 5 = 3.02754Check: OK
3)Check: OK
5) Check: OK
Section 2-2 – Basic Skills and Concepts
1) What is a frequency distribution and why is it useful?
A frequency distribution uses some type of method for listing data values and their corresponding counts (or frequencies). A frequency distribution is useful for organizing data, looking for patterns, and visualizing the data.Check: OK
5) Identify the class width, class midpoints, and class boundaries for the frequency distribution:
Daily Low Temp (F) / Frequency35-39 / 1
40-44 / 3
45-49 / 5
50-54 / 11
55-59 / 7
60-64 / 7
65-69 / 1
Class Width: 5
Class Midpoints: 37, 42, 47, 52, 57, 62, and 67
Class Boundaries: 34.5, 39.5, 44.5, 49.5, 54.5, 59.5, 64.5, and 69.5 Check: OK
9) Does the frequency distribution given in Exercise 5 appear to have normal distribution?
The two general criteria for a normal distribution are: 1) frequency start low, reach a maximum, and then finish low; and 2) symmetry. In the case, the distribution does appear to be normal. Check: OK
Section 2-3 – Basic Skills and Concepts
1) What important characteristic of data can be better understood through examination of histogram?
A histogram gives a visual representation of the shape (i.e. normal, skewed, etc.) of the distribution.Check: OK
5) How many crew members are included in the histogram (on page 54 of the text)?
2 + 10 + 5 + 1 = 18 crew membersCheck: OK
11) Refer to Exercise 19 in Section 2-2 anduse the frequency distribution to construct a histogram. Do the data appear to be normal?
Rainfall (Inches) / Frequency0.00-0.24 / 46
0.25-0.49 / 5
0.50-0.74 / 0
0.75-0.99 / 0
1.00-1.24 / 0
1.25-1.49 / 1
The two general criteria for a normal distribution are: 1) frequency start low, reach a maximum, and then finish low; and 2) symmetry. In the case, the distribution does not appear to be normal since it is skewed in one direction. Check: OK
15) Refer to Exercise 23 in Section 2-2 and use the frequency distribution for the weights of the pre-1983 pennies to construct a histogram. Do the weights appear to be normal?
Coin Weights (Grams) / Frequency2.9500-2.9999 / 2
3.0000-3.0499 / 3
3.0500-3.0999 / 22
3.1000-3.1499 / 7
3.1500-3.1999 / 1
The two general criteria for a normal distribution are: 1) frequency start low, reach a maximum, and then finish low; and 2) symmetry. In the case, the distribution does appear to be normal. Check: OK
17) Refer to Table 2-8 and use the relative frequency distribution for the best actors to construct a relative frequency histogram. Do the two genders appear to win Oscars at different ages?
Although there are similarities between the graphs, it appears that men tend to win Oscars at slightly older ages than women. Check: OK
Section 2-4 – Basic Skills and Concepts
1) What is the main objective in graphing data?
The main objective of a graph is to visually depict data in a manner that emphasizes the key characteristics or features of the data.Check: OK The graph can also show the distribution, outliers, and so forth.
9) Use the heights (Data Set 11) to construct and stemplot. What does the stemplot suggest about the distribution of heights?
Height of Eruptions of Old FaithfulStems (Tens) / Leaves (Ones)
9 / 55
10
11 / 00055
12 / 000000005555
13 / 0000000066668
14 / 000088
15 / 00
The distribution of the eruption heights of Old Faithful appear to be approximately normal.Check: OK
17) Use the data to create a scatter diagram. In Data Set 3, use tar for the horizontal scale and use carbon monoxide (CO) for the vertical scale. Determine whether there appears to be a relationship between cigarette tar and CO. If so, describe the relationship.
In general, it appears that as the amount of tar increases, the amount of carbon monoxide (CO) also increases. Check: OK
Unit 2 – Review Exercises
1) Construct a frequency distribution of the ages of the Oscar-winning actors listed in Table 2-1. Use the same class intervals that were for the actresses. How does the result compare to the frequency distribution for actresses?
Frequency Distribution: Ages of Best ActorsAge of Actor / Frequency
21-30 / 3
31-40 / 25
41-50 / 30
51-60 / 14
61-70 / 3
71-80 / 1
It appears that the distribution for the actors is centered at a value that is slightly higher than for actresses which means that males to win Oscars at older ages as compared to females.Check: OK
3) Construct a dotplot of the ages of the Oscar-winning actors listed in Table 2-1. How does the result compare to the dotplot for actresses?
Although the shape of the distribution is similar to the dotplot for the actresses, the values for the males tend to be concentrated at a higher age.Check: OK
5) Refer to Table 2-1 and use only the first 10 ages of actresses and the first 10 ages of the actors. Construct a scatterplot. Based on the result, does there appear to be an association between the ages of actresses and the ages of actors?
The points do not form any type of consistent pattern (i.e. a line, parabolic curve, etc.). Therefore, there does not appear to be an association between the ages of the two groups. Check: OK I needed to reference the answer in order to clarify how the variables were related.
Unit 2 – Cumulative Review Exercises
1) Consider the numbers that result from spins. Do those numbers measure or count anything?
No. These numbers are the values that are obtained. The number of times (the frequency) each value is spun is what is counted.Check: OK
3) Examine the distribution table. Given that the last class summarizes results from three slots, is its frequency approximately consistent with the results that would be expected from an unbiased roulette wheel? In general, do the frequencies suggest that the wheel is unbiased?
The other classes each represent five spaces on the wheel. Since the last class only involves three slots, this is 60% of the size of the other classes. If you divide 25 (the frequency) by 0.6, you get a value of 41.666666 or 42. This value seems to be relatively consistent with the other values.
Given the fact that only 380 spins were used, I would say that the roulette wheel is unbiased. In the long run, the values should even out and be consistent for all of the classes.Check: OK
Section 3-2 – Basic Skills and Concepts
1) In what sense are the mean, median, mode, and midrange measures of “center”?
Each of these measurements attempts to give an indication of the value that a distribution is centered around. The mean locates the center by dividing the sum of all values by the number of values in the distribution. The median is simply the middle number in an ordered list of values. The mode is the value that appears the most. The midrange is the average of the two extreme (maximum and minimum) values. Check: OK
9) Find the mean, median, mode, and midrange. Fourteen different second-year medical students at BellevueHospital measured the blood pressure of the same person. The systolic readings are listed. What is notable about this data set?
Mean: Check: OK
Median: 120 120 125 130 130 130 130 135 138 140 140 143 144 150
Check: OK
Mode: 130Check: OK
Midrange:Check: OK