Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 19, Problem 45E
Grades, again In some situations where the expected cell counts are too small, as in the case of the grades given by Professors Alpha and Beta in Exercise 43, we can complete an analysis anyway. We can often proceed after combining cells in some way that makes sense and also produces a table in which the conditions are satisfied. Here, we create a new table displaying the same data, but calling D’s and F’s “Below C”:
| Prof. Alpha | Prof. Beta | |
| A | 3 | 9 |
| B | 11 | 12 |
| C | 14 | 8 |
| Below C | 12 | 3 |
- a) Find the expected counts for each cell in this new table, and explain why a chi-square procedure is now appropriate.
- b) With this change in the table, what has happened to the number of degrees of freedom?
- c) Test your hypothesis about the two professors, and state an appropriate conclusion.
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Suppose you are interested in seeing whether the total number of days students are absent from high school correlates with their grades. You obtain
school records that list the total absences and average grades (on a percentage scale) for 80 graduating seniors.
You decide to use the computational formula to calculate the Pearson correlation between the total number of absences and average grades. To do so,
you call the total number of absences X and the average grades Y. Then, you add up your data values (ZX and EY), add up the squares of your data
values (EX² and ΣY²), and add up the products of your data values (ΣXY). The following table summarizes your results:
ΣΧ
380
ΣΥ
5,820
⠀
ΣΧ2 2,708
ΣΥ2
440,838
ΣΧΥ
26,709
The sum of squares for the total number of absences is SSx
=
The sum of squares for average grades is SSy
=
The sum of products for the total number of absences and average grades is SP =
The Pearson correlation coefficient is r =
Suppose you want to predict average grades…
Chapter 19 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 19.3 - Why do we need the control group?Ch. 19.3 - Prob. 2JCCh. 19.3 - Prob. 3JCCh. 19.3 - Prob. 4JCCh. 19.3 - Prob. 5JCCh. 19.3 - Prob. 6JCCh. 19.4 - Prob. 7JCCh. 19.4 - Prob. 8JCCh. 19.4 - Prob. 9JCCh. 19 - Human births If there is no seasonal effect on...
Ch. 19 - Bank cards At a major credit card bank, the...Ch. 19 - Prob. 3ECh. 19 - Prob. 4ECh. 19 - Customer ages An analyst at a local bank wonders...Ch. 19 - Bank cards, once more A market researcher working...Ch. 19 - Human births, last time For the data in Exercise...Ch. 19 - Prob. 8ECh. 19 - Iliad injuries 800 BCE Homers Iliad is an epic...Ch. 19 - Prob. 10ECh. 19 - Prob. 11ECh. 19 - Prob. 12ECh. 19 - Dice After getting trounced by your little brother...Ch. 19 - MMs As noted in an earlier chapter, Mars Inc. says...Ch. 19 - Nuts A company says its premium mixture of nuts...Ch. 19 - Prob. 16ECh. 19 - NYPD and race Census data for New York City...Ch. 19 - Violence against women In its study When Men...Ch. 19 - Fruit flies Offspring of certain fruit flies may...Ch. 19 - Prob. 20ECh. 19 - Prob. 21ECh. 19 - Lottery numbers The fairness of the South African...Ch. 19 - Prob. 23ECh. 19 - Prob. 24ECh. 19 - Childbirth, part 2 In Exercise 23, the table shows...Ch. 19 - Prob. 26ECh. 19 - Prob. 27ECh. 19 - Prob. 28ECh. 19 - Prob. 29ECh. 19 - Does your doctor know? (part 4) In Exercises 24,...Ch. 19 - Prob. 31ECh. 19 - Prob. 32ECh. 19 - Prob. 33ECh. 19 - NYPD The table below shows the rank attained by...Ch. 19 - Prob. 35ECh. 19 - NYPD again Examine and comment on this table of...Ch. 19 - Cranberry juice Its common folk wisdom that...Ch. 19 - Prob. 38ECh. 19 - Montana A poll conducted by the University of...Ch. 19 - Fish diet Medical researchers followed 6272...Ch. 19 - Prob. 41ECh. 19 - Working parents In April 2009, Gallup published...Ch. 19 - Grades Two different professors teach an...Ch. 19 - Full moon Some people believe that a full moon...Ch. 19 - Grades, again In some situations where the...Ch. 19 - Full moon, next phase In Exercise 44, you found...Ch. 19 - Racial steering A subtle form of racial...Ch. 19 - Survival on the Titanic Newspaper headlines at the...Ch. 19 - Prob. 49ECh. 19 - Education by age Use the survey results in the...
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardUrban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
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