# Discovering Statistics and Data, Third Edition

## Errata

Errata in Discovering Statistics and Data by James S. Hawkes

### Chapter 1

#### Section 1.3

##### Page 8:

The third bullet item should read: "In 2017, $8.6$ trillion text messages were sent annually worldwide, and $4$ million text messages were sent each minute in the US."

##### Page 9:

The second sentence of the last paragraph should have a period at the end of the sentence: "One satellite, however, can produce enormous quantities of data."

##### Page 10:

In the margin content titled "The Host with the Most," the last sentence should be "However, only about $85\%$ are thought to use the internet regularly."

### Chapter 3

#### Section 3.1

##### Page 78:

The third sentence of the last paragraph should not have a comma after 'table'.

#### Section 3.2

##### Page 83:

Figure 3.2.5 should have vertical gridlines running through each tickmark on the `x`-axis.

#### Section 3.4

##### Page 100:

In the first sentence of Example 3.4.1 there should be dashes between the words in 'stem and leaf'.

#### Section 3.5

##### Page 114:

In the Prison Population graph, the 6^{th} label on the horizontal axis should be 'Thailand' instead of 'Thiland'.

### Chapter 4

#### Section 4.1

##### Page 135:

Change the order of the last two pairs of numbers in the numerator of the weighted mean calculation in part **a.** to follow the formula with weights being the first number multiplied in each pair:
$3\cdot 3+4\cdot 4+5\cdot 2+3\cdot 4$.

##### Page 135:

Change the order of the last two pairs of numbers in the numerator of the weighted mean calculation in part **b.** to follow the formula with weights being the first number multiplied in each pair:
$3\cdot 3+4\cdot 4+5\cdot x+3\cdot 4$.

#### Section 4.3

##### Page 162:

The steps for Finding the `P`^{th} Percentile should be numbered from
$1$ to
$3$. Each sentence of the procedure is a step.

##### Page 166:

The author's last name in the article "The Zen of Statistics" should be 'Hofstadter' instead of 'Hofstadler'.

##### Page 167:

In Figure 4.3.3, the first quartile should be '$41$' instead of '$42$'.

##### Page 168:

In Figure 4.3.4, there should be an outlier of $59$ on the Yankees box plot.

#### Section 4.4

##### Page 178:

The word 'figure' should be 'figures' in the last sentence on the page.

### Chapter 5

#### Section 5.2

##### Page 223:

The sentence under the top left figure in Figure 5.2.4 should read: "As `x` increases `y` tends to increase."

##### Page 224:

The sentence above Figure 5.2.6 should be moved to the end of the sentence immediately below the figure.

##### Page 224:

In Figure 5.2.5, the slope of the line is off slightly. The line should be steeper and clearly go through points $\left(1,5\right)$ and $\left(2,7\right)$.

#### Section 5.4

##### Page 248:

The `y`-values of the data points on the graph "Percent of Overweight Americans Based on BMI" vary slightly from the `y`-values in the table.

##### Page 249:

The `y`-values of the data points on the graph "Percent of Overweight Americans Based on BMI" with the trend line, vary slightly from the `y`-values in the table.

#### Section 5.5

##### Page 252:

In the Technology tip in the margin, replace 'Tableau' with 'Microsoft Excel.'

### Chapter 6

#### Section 6.1

##### Page 271:

In the Summary box, the formula for the relative frequency of the event "getting a head" should be: $A:{\displaystyle \frac{k}{n}}={\displaystyle \frac{718}{1450}}\approx 0.4952$ .

##### Page 273:

The first sentence of Example 6.1.2 should read: "In Experiment 3, let A be the event of observing an even number when rolling a six-sided die."

#### Section 6.2

##### Page 279:

In the definition for Probability Law 4 the first sentence should read "The sum of the probabilities of all outcomes in a sample space must equal one." In the next sentence replace 'event' with 'outcome'.

#### Section 6.4

##### Page 305:

In Exercise 5 the word 'desert' should be 'dessert'.

### Chapter 7

#### Section 7.5

##### Page 348:

There should be a thick line representing the bar for $x=3$ in Figure 7.5.1.

##### Page 349:

The tickmarks on the `x`-axis should be removed in Figure 7.5.3.

##### Page 351:

The second sentence in the solution should read: "Based on previous experience, we assume that the number of defects is approximated by a Poisson distribution with Poisson parameter `λ` as follows."

### Chapter 8

#### Section 8.1

##### Page 367:

In the second sentence of Example 8.1.1 the word 'the' should be inserted before 'distribution.'

#### Section 8.4

##### Page 386:

In Example 8.4.1, the first equation in the solution should be:

$P\left(10<x<40\right)=P\left({\displaystyle \frac{\left(10-10\right)}{20}<\frac{x-\mu}{\sigma}<\frac{\left(40-10\right)}{20}}\right)=P\left(0<z<1.5\right)$

#### Section 8.5

##### Page 394:

The third word in the Normal Probability Plot definition should be 'probability' instead of 'probabilty'.

##### Page 398:

The first sentence below the bar graph should read "Clearly, the histogram does not have a bell shape, so we would reject the belief that bill-length ratio is normally distributed."

#### Section 8.6

##### Page 403:

In the solution of Example 8.6.1, the bar above 18 appears filled in (when you zoom out) and shouldn't be.

### Chapter 9

#### Section 9.4

##### Page 436:

There should be a header at the top of this page titled "Is There a Familiar Pattern to the Variability of $\hat{p}$?".

##### Page 436:

The sentence before Example 9.4.1 should read: "Since the sampling distribution of $\hat{p}$ is known, probabilities for various errors of estimation can be determined."

##### Page 436:

The second sentence of Example 9.4.1 should be "If the true proportion in the population that prefers Pepsi is really $0.5$, what is the probability that less than $0.44$ of the persons in the sample will prefer Pepsi?"

##### Page 438:

The sentence in Example 9.4.2 prior to the graph of the distribution of $\hat{p}$ should read: "To find the probability that $\hat{p}$ is within $0.05$ of the true proportion, we must find….."

### Chapter 10

#### Section 10.2

##### Page 459:

The last sentence prior to Table 10.2.1 should have the parentheses removed from around $1-\alpha $.

##### Page 461:

The last part of the technology tip in the margin should have you navigate to **Technology Instructions > Confidence Intervals > z-Interval**.

##### Page 462:

The output at the top of the page should be titled "One-Sample `Z` Descriptive Statistics." The value under SE Mean should be
$1.325$ and the
$95\%$ CI
for `μ` should be
$\left(144.98,150.18\right)$.

##### Page 462:

The values for the endpoints of the confidence interval at the end of the last sentence in Example 10.2.2 should be $144.98$ instead of $144.95$ and $150.18$ instead of $150.21$.

##### Page 462:

In the first paragraph of the section following Example 10.2.2, the word 'variance' should be replaced with 'standard deviation' in both sentences.

##### Page 465:

In the first sentence of the second paragraph, remove '$n<30$' and replace with "the population is approximately normally distributed".

#### Section 10.3

##### Page 472:

In the variable description of the proportion below the third paragraph there is a typo. Replace 'posses' with 'possess'.

##### Page 474:

In the second sentence of the Solution to Example 10.3.2, replace $p$ with $\hat{p}$. The sentence should read: "Note our sample is large enough such that $n\hat{p}=48>10$ and $n\left(1-\hat{p}\right)=362>10$."

#### Section 10.4

##### Page 483:

The expression between the last two paragraphs of the solution of Example 10.4.1 should be $0.0275<\sigma <0.0730$.

### Chapter 11

#### Section 11.1

##### Page 493:

Under the subheading titled "The Correct Formulation of the Null Hypothesis…", the next to last sentence should have the word 'the' removed prior to the word 'contradict' so that the sentence reads: "Because the null hypothesis is presumed to be true, this hypothesis is not rejected unless there is overwhelming evidence to contradict ${H}_{0}$."

##### Page 494:

In Example 11.1.2, replace the last sentence of the first paragraph with the sentence "What are the correct hypotheses?".

#### Section 11.2

##### Page 509:

Under the procedure titled "Performing a Hypothesis Test Using `P`-Values," the second bulleted item should read "If the computed `P`-value is greater than or equal to
$\alpha $, fail to reject the null hypothesis.

##### Page 509:

In the first sentence under Step 4 of Returning to Example 11.2.1, replace 'critical value' with 'test statistic.'

##### Page 510:

In the first sentence below the figure at the top of the page replace the `P`-value
$0.0038$
with
$0.0076$.

##### Page 510:

In Step 5 replace the `P`-value
$0.0038$ with
$0.0076$.

##### Page 512:

In the figure at the bottom of the page there should be a vertical line at $2.53$ separating the two shaded regions.

##### Page 513:

In the sentence prior to the procedure box, the word 'statistics' should be 'statistic.'

##### Page 514:

The title at the top of the page should have the question mark removed.

##### Page 514:

The next to last sentence in the first paragraph should read: "Some of the technical details concerning the distribution of the test statistic change, since the sample standard deviation, `s`, will be used in place of the population standard deviation,
$\sigma $."

#### Section 11.4

##### Page 533:

In the procedure box the 't' in 'two-tailed test' should be in bold font.

#### Section 11.5

##### Page 541:

The variable definitions at the bottom of the procedure box should have commas at the end of the first three lines following 'where,'.

#### Section 11.6

##### Page 545:

The fourth sentence of the solution to Example 11.6.1 should read: "Considering that a test statistic this large would result from ordinary sampling variation is only about eight in a million samples, ...".

### Chapter 12

#### Section 12.1

##### Page 560:

The correct source for the margin content titled "Hypothesis Testing Is Not Loved by All Statisticians" is an unpublished article by Marks R. Nester titled "A Myopic View and History of Hypothesis Testing."

##### Page 562:

The Greek letter $\sigma $ after 'same' should be removed from the third sentence of Example 12.1.2.

##### Page 563:

In the note in the margin the alternative hypothesis should be ${H}_{a}$: ${u}_{1}>{u}_{2}$

##### Page 568:

The first word after the procedure box should be 'Provided' instead of 'Providing'.

##### Page 571:

The scale of the boxplot graph at the top of the page should have a `y`-axis scale that starts at
$0$ with increments of
$0.5$.

#### Section 12.2

##### Page 593:

In the statement of the hypotheses above Step 2, the three occurrences of '$100$ proof' should be '$100$-proof'.

##### Page 594:

The `t`-distribution curve in Step 4 should have a tickmark below the mean with a label of
$0$.

#### Section 12.3

##### Page 602:

In the first sentence of the Technology tip in the margin, the word 'calculated' should replace 'calulated'.

### Chapter 13

#### Section 13.2

##### Page 621:

In Example 13.2.1, the equation $y=-1412.23x+19198.32$ should not be on the graph.

##### Page 624:

In the second Note, there should be a period at the end of the sentence: "We are $95\%$ confident in the procedure."

### Chapter 14

#### Section 14.4

##### Page 667:

In the sentence before the properties box, the comma should be removed between 'values' and 'for'.

##### Page 669:

The content in the two procedure boxes should be contained in one box and the heading of the second box removed.

##### Page 669-670:

The three sentences following the procedure box on page 669 and continuing to the next page should be removed.

##### Page 670:

In the first full paragraph on the page, there should be a question mark at the end of the fifth sentence: "The fundamental question is how large must the `F`-value be in order to believe the model has some explanatory power?"

##### Page 670:

In the sentence in parentheses above Step 4, SST should be Total SS.

##### Page 670:

In the bottom row of the Analysis of Variance table, SST should be Total SS.

##### Page 670:

In the last paragraph, the first sentence should read: "If the value of the `F`-statistic falls in the rejection region or the `P`-value for the test statistic is less than
$\alpha $, then reject the null hypothesis." The next sentence should read: "If not, then do not reject the null hypothesis."

##### Page 672:

In the sentence above the definition box, the first occurrence of "${b}_{1}$" should be "${\beta}_{i}$" and the second occurrence should be "${\beta}_{1}$".

### Chapter 15

#### Section 15.1

##### Page 706:

In the second sentence below the formula box for the Sum of Squares for Treatments, the notation in parentheses for the treatment means should be ${\stackrel{\_}{x}}_{j}$ instead of ${\stackrel{\_}{x}}_{i}$.

##### Page 715:

The first sentence of Step 5 should read as follows: "Since the resulting value of the test statistic, $0.9286$, is less than the critical value of $4.2565$, we fail to reject the null hypothesis." At the end of the following sentence the 'P' in 'P-value' should be italicized.

##### Page 715:

The second sentence of Step 6 should read: "Thus, we cannot conclude that there is a difference in average sale price among the three sales reps."

### Chapter 16

#### Section 16.1

##### Page 759:

In exercise 13 remove 'a' in front of '30-year' in the first sentence.

#### Section 16.2

##### Page 762:

The period following the expression for $E\left({n}_{1}\right)$ at the top of the page should be removed.

##### Page 766:

The shape of the graph is not accurate for a chi-square distribution with 2 degrees of freedom.

### Chapter 17

#### Section 17.1

##### Page 791:

In the solution of Example 17.1.2, there should be a colon after "Step 1" in the sentence: "Step 1: Determine the null and alternative hypotheses."

#### Section 17.2

##### Page 797:

The third and fourth sentences below the table in Example 17.2.1 should be modified to read as follows: "The next lowest-priced stock is AT&T Inc., which is assigned a rank of 2. The highest-priced stock is 3M Co., which has a rank of 9."

##### Page 801:

In the procedure box the heading 'Hypothesis:' should be 'Hypotheses:'.

#### Section 17.3

##### Page 809:

The first sentence under the heading Assumptions in the procedure box should read: "Data is such that it can be ranked."

##### Page 809:

In the procedure box the heading 'Hypothesis:' should be 'Hypotheses:'.

#### Section 17.5

##### Page 820:

The sentence above the diagram in the solution for part **a.** of Example 17.5.1 should have 'a' before
'$0.05$ level of significance.'

##### Page 820:

The sentence above the diagram in the solution for part **b.** of Example 17.5.1 should have 'a' before
'$0.05$ level of significance.'

##### Page 821:

The first sentence of the solution in Example 17.5.2 should have 'a' before '$5\%$ level of significance, ...'.

#### Section 17.6

##### Page 825:

In the last paragraph, the second sentence should read: "The critical value can be found in Table G of Appendix A as ${\chi}_{\left(3-1\right),0.05}^{2}=5.991$.".

##### Page 826:

The rank sums for each type of brake pad in the table of Example 17.6.2 should be under the Rank columns.

##### Page 827:

The first sentence should read: "Referring to Appendix A, Table G, we can see that ${\chi}_{2,0.05}^{2}=5.991$.".

### Answer Key

#### Section 11.1

##### Exercise 21:

In part **b.**, Critical values
=$-2.201$,
$2.201$.