Chapter 3: Problem 53
What makes the range less desirable than the standard deviation as a measure of dispersion?
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Chapter 3: Problem 53
What makes the range less desirable than the standard deviation as a measure of dispersion?
These are the key concepts you need to understand to accurately answer the question.
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Find the population mean or sample mean as indicated. Population: 3,6,10,12,14
The average 20 - to 29 -year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20 - to 29 -year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 67-inch man or a 62 -inch woman?
The data in the next column represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. The "flipped" classroom is one where the content is delivered via video and watched at home, while class time is used for homework and activities. $$ \begin{array}{llllllll} \hline \text { Traditional } & 70.8 & 69.1 & 79.4 & 67.6 & 85.3 & 78.2 & 56.2 \\\ & 81.3 & 80.9 & 71.5 & 63.7 & 69.8 & 59.8 & \\ \hline \text { Flipped } & 76.4 & 71.6 & 63.4 & 72.4 & 77.9 & 91.8 & 78.9 \\ & 76.8 & 82.1 & 70.2 & 91.5 & 77.8 & 76.5 & \end{array} $$ (a) Determine the mean and median score for each class. Comment on any differences. (b) Suppose the score of 59.8 in the traditional course was incorrectly recorded as \(598 .\) How does this affect the mean? the median? What property does this illustrate?
Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked \(\mathrm{A}, \mathrm{B}, \mathrm{C},\) and D. Cards in decks \(A\) and \(B\) had a point value of 100 while cards in decks \(C\) and \(D\) had point values of \(50 .\) However, deck A had penalty cards that deducted points between 150 and \(300 ;\) deck \(B\) had one penalty card of \(1250 ;\) deck \(C\) had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks \(C\) and \(D\) and in the long haul, decks \(C\) and \(D\) resulted in more points than decks \(A\) and \(B\). In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks \(\mathrm{C}\) and \(\mathrm{D}\) out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks \(\mathrm{C}\) and \(\mathrm{D}\). The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impulsivity (e.g., "I do things without thinking"). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group \(1 .\) After analysis of the data, it was determined that the mean number of advantageous cards (decks \(C\) and \(D\) ) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group \(1 .\) The researchers concluded that hunger improves advantageous decision making. Source: de Ridder, D., Kroese, F., Adriaanse, M., \& Evers, C. "Always Gamble on an Empty Stomach: Hunger Is Associated with Advantageous Decision Making," PLOS One \(9(10) .\) doi: 10.1371 /journal. pone. \(0111081 .\) (a) What type of experimental design is this? (b) Identify the experimental units. (c) What is the response variable? Is it qualitative or quantitative? If quantitative, is it discrete or continuous? (d) What factors that might impact the response variable are cited in the article? Which factor is manipulated? How many levels are there for the manipulated factor? (e) What role does randomization play in the study? How do the researchers verify that randomization resulted in similar groups prior to the treatment? (f) What are the statistics in the study? (g) What is the conclusion of the study?
Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students in Professor Alpha's class have a mean score of \(80 \%\) with a standard deviation of \(5 \%,\) while past students in Professor Omega's class have a mean score of \(80 \%\) with a standard deviation of \(10 \% .\) Decide which instructor to take for Introductory Biology using a statistical argument.
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