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. Calculate the least-squares line. Put the equation in the form ŷ = a + bx. e. Find the correlation coefficient. What does it imply about the significance of the relationship? f. Find the estimated areas for Alabama and for Colorado. Are they close to the actual areas? g. Use the two points in Part F to plot the least... |
Correlation Group x (no. of hours spent studying) y (final exam grades) Median x value Median y value Table 12.38 19 ŷ = 2.23 + 1.99x 45 50 51 65 72 80 90 96 2 4.5 7 50 68.5 90 21 The slope is 1.99 (b = 1.99). It means that for every endorsement deal a professional player gets, he gets an average of another $1.99 mill... |
: ŷ (number of flu cases) = –3,448,225 + 1749.777 (year). This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 753 Coefficients Intercept –3,448,225 x Variable 1 1,749.777 Table 12.39 47 • a = –3,488,225 • b = 1,750 • correlation = 0.4526 • n = 2... |
41 Table 12.41 50 60 62 65 67 70 71 86 87 90 98 294.5 364 61 70 605.5 88.5 The ordered pairs are (294.5, 61), (364, 70), and (605.5, 88.5). The slope can be calculated using the formula m = y3 − y1 x3 − x1. Substituting the median x and y values, from the first and third groups gives m = 88.5 − 61 605.5 − 294.5, which ... |
a p value = 0.4736, so we do not reject; there is a not a significant linear relationship between page and discount. Using the table of critical values for the correlation coefficient, with seven gives degrees of freedom, the critical value is 0.666. The correlation coefficient xi = –0.2752 is not less than 0.666, so ... |
percentage of new birds in the colony decreases by 30.3 percent. d. If we examine r2, we see that only 57.52 percent of the variation in the percentage of new birds is explained by the model and the correlation coefficient, r = –.7584 only indicates a somewhat strong correlation between returning and new percentages. ... |
y-intercept becomes more meaningful. 72 If we remove the two service academies (the tuition is $0.00), we construct a new regression equation of y = –0.0009x + 160, with a correlation coefficient of 0.71397 and a coefficient of determination of 0.50976. This allows us to say there is a fairly strong linear association... |
c. The relationship does not appear to be linear. d. ŷ = –745.252 + 54.75569x. e. r =.8944 and yes, it is significant. f. 32-inch: $1006.93, 50-inch: $1992.53. g. No, the relationship does not appear to be linear. However, r is significant. h. No, the 60-inch TV. i. For each additional inch, the price increases by $54... |
265. g. Yes. h. No, (1987, 62.7). i. 72.5937, no. j. Slope = 0.1656. As the year increases by one, the percent of workers paid hourly rates tends to increase by 0.1656. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 759 76 a. Size (ounces) ... |
: 46,407.576 square miles, Colorado: 62,575.224 square miles. g. The Alabama estimate is closer than the Colorado estimate. h. If the outlier is removed, there is a linear relationship. i. There is one outlier (Hawaii). j. rank 51: 75,711.4 square miles, no. 760 k. Chapter 12 | Linear Regression and Correlation Alabama... |
simplest form of ANOVA called single factor or oneway ANOVA. You will also study the F distribution, used for one-way ANOVA, and the test of two variances. This is a very brief overview of one-way ANOVA. You will study this topic in much greater detail in future statistics courses. One-way ANOVA, as it is presented he... |
b) We reject H0 as all the means are not the same; the differences are too large to be due to random variation. 13.2 | The F Distribution and the F Ratio The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic i... |
= the number of different groups • nj = the size of the jth group • sj = the sum of the values in the jth group • n = total number of all the values combined (total sample size: ∑nj) • x = one value: ∑x = ∑sj • Sum of squares of all values from every group combined: ∑x2 • Between group variability: SStotal = ∑x2 – ⎛ ⎝... |
have equal variances. F Ratio or F Statistic F = MSbetween MSwithin If MSbetween and MSwithin estimate the same value, following the belief that H0 is true, then the F ratio should be approximately equal to 1. Mostly, just sampling errors would contribute to variations away from 1. As it turns out, MSbetween This Open... |
2 = 15, s3 = 15.5 Following are the calculations needed to fill in the one-way ANOVA table. The table is used to conduct a hypothesis test. 766 Chapter 13 | F Distribution and One-way Anova SS(between) = ∑ (s j) ⎞ ⎛ ⎝∑ s j ⎠ n = 2 s1 4 2 s2 3 + + 2 s3 3 (s1 + s2 + s3)2 10 − where n1 = 4, n2 = 3, n3 = 3, and n = n1 + n2... |
– k = 10 total data – 3 groups = 7 n – 1 = 10 total data – 1 = 9 Error (Within) Total Table 13.3 F = MS(Factor)/MS(Error) = 1.1229/2.9792 = 0.3769 MS(Factor) = SS(Factor)/(k – 1) = 2.2458/2 = 1.1229 MS(Error) = SS(Error)/(n – k) = 20.8542/7 = 2.9792 This OpenStax book is available for free at http://cnx.org/content/co... |
denominator get larger, the curve approximates the normal. • Other uses for the F distribution include comparing two variances and two-way analysis of variance. Two-way analysis is beyond the scope of this chapter. 768 Chapter 13 | F Distribution and One-way Anova Figure 13.3 Example 13.2 Let’s return to the slicing t... |
to be due to chance alone. We may conclude that at least some of the mulches led to different mean yields. To find these results on the calculator: Press STAT. Press 1:EDIT. Put the data into the lists L1,L2,L3,L4,L5. Press STAT, arrow over to TESTS, and arrow down to ANOVA. Press ENTER, and then enter (L1,L2,L3,L4,L5... |
2.26 3.18 Table 13.7 Mean Grades for Four Sororities Using a significance level of 1 percent, is there a difference in mean grades among the sororities? Solution 13.3 Let μ1, μ2, μ3, μ4 be the population means of the sororities. Remember that the null hypothesis claims that the sorority groups are from the same normal... |
at http://cnx.org/content/col30309/1.8 Chapter 13 | F Distribution and One-way Anova 773 Basketball Baseball Hockey Lacrosse 3.6 2.9 2.5 3.3 3.8 2.1 2.6 3.9 3.1 3.4 4.0 2.0 2.6 3.2 3.2 2.0 3.6 3.9 2.7 2.5 Table 13.8 GPAs for four sports teams Use a significance level of 5 percent and determine if there is a difference... |
¯ Calculate the mean of the three sample variances (11.7, 18.3, and 16.3). Mean of the sample variances = 15.433 = s2 then MSwithin = s2 pooled = 15.433. pooled, The F statistic (or F ratio) is F = MSbetween MSwithin = 2 ns x¯ s2 pooled = (5)(0.413) 15.433 = 0.134. The dfs for the numerator = the number of groups – 1 =... |
distribution is testing two variances. It is often desirable to compare two variances rather than two averages. For instance, college administrators would like two college professors grading exams to have the same variation in their grading. For a lid to fit a container, the variation in the lid and the container shou... |
, s1 variance causes the ratio (s1)2 (s2)2 to be greater than 1. If s1 2 and s2 2 are far apart, then F = (s1)2 (s2)2 is a large number. 2 and s2 2 tend to be very different, too. Choosing s1 2 as the larger sample Therefore, if F is close to 1, the evidence favors the null hypothesis (the two population variances are ... |
Make a decision: Since α > p-value, reject H0. Conclusion: With a 10 percent level of significance from the data, there is sufficient evidence to conclude that the variance in grades for the first instructor is smaller. Press STAT and arrow over to TESTS. Arrow down to D:2-SampFTest. Press ENTER. Arrow to Stats (89.9)... |
ute the following: a. Fruit i. ii. x¯ = ______ s x = ______ iii. n = ______ b. Vegetables i. ii. x¯ = ______ s x = ______ iii. n = ______ c. Bread i. ii. x¯ = ______ s x = ______ iii. n = ______ 3. Find the following: a. df(num) = ______ 780 Chapter 13 | F Distribution and One-way Anova b. df(denom) = ______ 4. State t... |
-Way ANOVA Analysis of variance extends the comparison of two groups to several, each a level of a categorical variable (factor). Samples from each group are independent and must be randomly selected from normal populations with equal variances. We test the null hypothesis of equal means of the response in every group ... |
be used in conjunction with numerical techniques. Always look at your data! 13.4 Test of Two Variances The F test for the equality of two variances rests heavily on the assumption of normal distributions. The test is unreliable if this assumption is not met. If both distributions are normal, then the ratio of the two ... |
ACTICE 13.1 One-Way ANOVA Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled to perform a one-way ANOVA test. What are they? 1. Write one assumption. 2. Write another assumption. 3. Write a third assumption. 4. Write a fourth assumption. 5. Write the... |
player can jump (in inches). The results are shown in Table 13.15. Team 1 Team 2 Team 3 Team 4 Team 5 36 42 51 32 35 38 48 50 39 38 44 46 41 39 40 Table 13.15 26. What is the df(num)? 27. What is the df(denom)? 28. What are the sum of squares and mean squares factors? 29. What are the sum of squares and mean squares e... |
-value = ______ State the decisions and conclusions (in complete sentences) for the following preconceived levels of α. 41. α = 0.05 a. Decision: ____________________________ b. Conclusion: ____________________________ 42. α = 0.01 a. Decision: ____________________________ b. Conclusion: ____________________________ 13... |
ume that speeds are normally distributed. 56. State the null and alternative hypotheses. 57. What is the F statistic? 58. At the 5 percent significance level, what can we say about the cyclists’ variances? HOMEWORK This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 13 | F Distributi... |
x¯ = s2 = Table 13.20 H0: µ1 = µ2 = µ3 = µ4 = µ5 Hα: At least any two of the group means µ1, µ2, …, µ5 are not equal. 61. degrees of freedom – numerator: df(num) = _________ 62. degrees of freedom – denominator: df(denom) = ________ 63. F statistic = ________ 13.3 Facts About the F Distribution DIRECTIONS Use a soluti... |
9.3 Use the following information to answer the next two exercises. Table 13.23 lists the number of pages in four different types of magazines. Home Decorating News Health Computer 172 286 163 205 197 Table 13.23 87 94 123 106 101 82 153 87 103 96 104 136 98 207 146 66. Using a significance level of 5 percent, test th... |
the three types of snow conditions? Suppose that Table 13.27 shows the results of a study. Powder Machine Made Hard Packed 1,210 1,080 1,537 941 Table 13.27 2,107 1,149 862 1,870 1,528 1,382 2,846 1,638 2,019 1,178 2,233 Assume that all distributions are normal, the four population standard deviations are approximatel... |
1.8 Chapter 13 | F Distribution and One-way Anova 793 73. DDT is a pesticide that has been banned from use in the United States and most other areas of the world. It is quite effective but persisted in the environment and over time proved to be harmful to higher-level organisms. Famously, egg shells of eagles and other... |
groups: Figure 13.9 794 Chapter 13 | F Distribution and One-way Anova 74. The data shown is the recorded body temperatures of 130 subjects as estimated from available histograms. Traditionally, we are taught that the normal human body temperature is 98.6 °F. This is not quite correct for everyone. Are the mean tempera... |
ariances 75. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed a... |
at the mall? Suppose that Table 13.34 shows the results of a study. Saturday Sunday Saturday Sunday 75 18 150 94 62 73 Table 13.34 44 58 61 19 99 60 89 62 0 124 50 31 118 137 82 39 127 141 73 80. Are the variances for incomes on the East Coast and the West Coast the same? Suppose that Table 13.35 shows the results of ... |
8 6.4 7.0 6.6 7.7 7.2 6.9 6.2 Table 13.37 Did the silver content of the coins change over the course of Manuel’s reign? Here are the means and variances of each coinage. The data are unbalanced. First Second Third Fourth Mean 6.7444 8.2429 4.875 5.6143 Variance 0.2953 1.2095 0.2025 0.1314 Table 13.38 798 Chapter 13 | F... |
. et al. (1994). A Handbook of Small Datasets. London: Chapman & Hall, p. 50. Hand. A Handbook of Small Datasets. p. 118. Mackowiak, P. A.,Wasserman, S. S., & Levine, M. M. (1992). A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderli... |
674 800 Chapter 13 | F Distribution and One-way Anova 55 Reject the null hypothesis. There is enough evidence to say that the variance of the grades for the first student is higher than the variance in the grades for the second student. 57 0.7414 59 SSbetween = 26 SSwithin = 441 F = 0.2653 62 df(denom) = 15 64 a. H0: µ... |
�s solution. h. i. Alpha: 0.05 ii. Decision: Do not reject the null hypothesis. iii. Reason for decision: p-value > alpha iv. Conclusion: There is not sufficient evidence to conclude that the mean numbers of daily visitors are different. 73 The data appear normally distributed from the chart and of similar spread. Ther... |
tailed test. g. Check student's solution. h. Decision: Do not reject the null hypothesis. i. Conclusion: There is insufficient evidence to conclude that the variances are different. 78 The answers may vary. Sample answer: Home decorating magazines and news magazines have different variances. 80 a. H0: = σ1 2 2 = σ2 2 2... |
MS) F Factor (between) Error (within) Total Table 13.43 344.16 1,219.55 1,563.71 3 – 1 = 2 14 – 3 = 11 14 – 1 = 13 172.08 110.87 1.5521 P(F > 1.5521) = 0.2548 Since the p-value is so large, there is not good evidence against the null hypothesis of equal means. We decline to reject the null hypothesis. Thus, for 2012, t... |
and third quartiles 8. Construct a histogram and box plot of the data. Chapter 4 Use the following information to answer the next two exercises. A recent poll concerning credit cards found that 35 percent of respondents use a credit card that gives them a mile of air travel for every dollar they charge. Thirty percent... |
, by individual members of a weight reducing clinic produced the following statistics: • Mean = 5 lbs • Median = 4.5 lbs • Mode = 4 lbs • Standard deviation = 3.8 lbs • First quartile = 2 lbs • Third quartile = 8.5 lbs What is the correct statement? A. One fourth of the members lost exactly two pounds. B. The middle 50... |
chance that he/she truly has the flu—and not just a nasty cold—is only about 4 percent. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu. 19. Define the random variable and list its possible values. 20. State the distribution of X. 21. Find the probabilit... |
in the number of the mothers that are employed. Let X = number of mothers that are employed. 30. State the distribution for X. 31. Find the probability that at least six are employed. 32. We expect the statistics discussion board to have, on average, 14 questions posted to it per week. We are interested in the number ... |
quartiles. Use them to construct a box plot of the data. Use the following information to answer the next three exercises. Table A3 shows data gathered from 15 girls on the Snow Leopard soccer team when they were asked how they liked to wear their hair. Supposed one girl from the team is randomly selected. Hair Style/... |
, five students from each high school class get full scholarships to four-year colleges. Assume that most high school classes have about 500 students. X = the number of students from a high school class that get full scholarships to four-year schools. Which of the following is the distribution of X? A. P(5) B. B(500, 5... |
that far. A. binomial B. uniform C. exponential D. normal 53. The length of time to brush one’s teeth is generally thought to be exponentially distributed with a mean of 3 4 minutes. Find the probability that a randomly selected person brushes his or her teeth less than 3 4 minutes. A..5 B. C. D. 3 4.43.63 54. Which d... |
is uniformly distributed between the three hour interval 4 p.m. to 7 p.m. Let X = the amount of time—hours—it takes for the first accident to occur. 59. What is the probability that the time of occurrence is within the first half-hour or the last hour of the period from 4 to 7 p.m.? A. It cannot be determined from the... |
A. 50 percent B. 35 percent C. 27.5 percent D. 75 percent 67. Are living in student housing within five miles of the campus and receiving some kind of financial aid mutually exclusive? A. Yes B. No C. Cannot be determined 68. The interest rate charged on the financial aid is ________ data. A. Quantitative discrete B. ... |
3.2.4.1 Table A4 75. Complete the cumulative frequency column. 76. Calculate the sample mean (a), the sample standard deviation (b), and the percent of the estimates that fall at or below four (c). 77. Calculate the median, M, the first quartile, Q1, and the third quartile Q3. Then construct a box plot of the data. 78.... |
exercises. In a survey at Kirkwood Ski Resort the following information was recorded. 0–10 11–20 21–40 40+ Ski 10 Snowboard 6 12 17 30 12 8 5 Table A6 Suppose that one person from Table A6 was randomly selected. 88. Find the probability that the person was a skier or was age 11–20. 89. Find the probability that the pe... |
. Use the following information to answer the next three exercises. A group of students measured the lengths of all the carrots in a five-pound bag of baby carrots. They calculated the average length of baby carrots to be 2.0 inches with a standard deviation of 0.25 inches. Suppose we randomly survey 16 five-pound bags... |
’s t distribution looks more like the graph of the standard normal distribution. C. If the number surveyed is 15, the normal distribution should never be used. Use the following information to answer the next five exercises. We are interested in the checking account balance of 24-old college students. We randomly surve... |
playing this game, what are your expected earnings? 115. • The mean grade on a math exam in Rachel’s class was 74, with a standard deviation of five. Rachel earned an 80. • The mean grade on a math exam in Becca’s class was 47, with a standard deviation of two. Becca earned a 51. • The mean grade on a math exam in Mat... |
822 Appendix A Californians wear jeans to work. Let C = Californian professional; NC = non-Californian professional A. State appropriate null and alternate hypotheses. B. Define the random variable. C. Calculate the test statistic and p-value. D. At the 5 percent significance level, what is your decision? E. What is t... |
72 in one trip to the supermarket? 127. Suppose five customers pool their money. How much money altogether would you expect the five customers to spend in one trip to the supermarket in dollars? 128. State the distribution to use if you want to find the probability that the mean amount spent by five customers in one tr... |
sample mean. 138. A math exam was given to all the fifth grade children attending Country School. Two random samples of scores were taken. The null hypothesis is that the mean math scores for boys and girls in fifth grade are the same. Conduct a hypothesis test. 824 Appendix A n ¯ x Boys 55 82 Girls 60 86 Table A8 s2 ... |
same value. 16. C The lowest data value is the median. 17..279 826 Appendix A 18. B No, I expect to come out behind in money. 19. X = the number of patients calling in claiming to have the flu, who actually have the flu. X = 0, 1, 2, …25 20. B(25,.04) 21..0165 22. 1 23. C Quantitative discrete 24. all words used by To... |
) =.72. Note the P(J AND K) = P(J)P(K) because J and K are independent. D. False – J and K are independent so P(J) = P(J|K). 46. A P(5) Chapter 7 47. A U(0, 4) 48. B 2 hours 49. A 1 4 50. A..7165 B. 4.16 C. 0 51. C 5 years 828 52. C exponential 53..63 54. A B(14,.20) 55. A B(14,.20) Chapter 8 56. C The mean amount of w... |
standard deviation than the distribution for X. 94. N ⎛ ⎝2,.25 16 ⎞ ⎠ 95. Answers will vary. 96..5000 97. 7.6 98. 5 99..9431 Appendix A 830 Chapter 11 100. 7.5 101..0122 102. N(7,.63) 103..9911 104. B exponential 105. A. True B. False C. False 106. Answers will vary. 107. Student’s t with df = 15 108. (560.07, 719.93)... |
(14,.60) 136. D Binomial 137..3669 138. p-value =.0006; reject the null hypothesis; conclude that the averages are not equal 139. p-value = 0; reject the null hypothesis; conclude that the proportion of males is higher 140. minimize α and β 141. A. no B. yes, P(M AND 30+) = 0 142. 12 38 143. no; p-value = 0 144. A unif... |
short survey, including information about how many times they have visited the club in the past week. 4. What kind of a sampling design is this? A. Cluster B. Stratified 834 C. Simple random D. Systematic 5. Number of visits per week is what kind of data? A. Qualitative B. Quantitative-continuous C. Quantitative-discr... |
35 15. The manager of a department store decides to measure employee satisfaction by selecting four departments at random, and conducting interviews with all the employees in those four departments. What type of survey design is this? A. Cluster B. Stratified C. Simple random D. Systematic 16. A popular American televi... |
The first is served a meal using normal-sized tableware, while the second is served the same meal but using tableware that it 20 percent smaller than normal. He records how much food is consumed by each group. Identify the following components of this study. A. population B. sample C. experimental units D. explanatory... |
1; 1; 1 2; 2; 2; 2; 2 3; 3; 3; 3; 3; 3; 3; 3 4; 4; 4; 4; 4; 4; 4; 4; 4 5; 5; 5; 5 31. You decide to construct a histogram of this data. What will be the range of your first bar, and what will be the central point? 32. What will be the widths and central points of the other bars? 33. Which bar in this histogram will be... |
the Center of the Data 45. In a marathon, the median finishing time was 3:35:04 (three hours, 35 minutes, and four seconds). You finished in 3:34:10. Interpret the meaning of the median time, and discuss your time in relation to it. Use the following information to answer the next three exercises. The values, in thous... |
the next two exercises. The following are probabilities describing a group of college students. Let P(M) = the probability that the student is male Let P(F) = the probability that the student is female Let P(E) = the probability the student is majoring in education Let P(S) = the probability the student is majoring in... |
week). 67. What is the probability a student studies less than 15 hours per week? 68. Are the events study at least 15 hours per week and makes the honor roll independent? Justify your answer numerically. 3.5: Tree and Venn Diagrams 69. At a high school, some students play on the tennis team and some play on the socce... |
possibility would be to obtain a roster of students enrolled in the college, including the class standing for each student. Then, you would draw a proportionate random sample from within each class. For instance, if 30 percent of the students in the college are freshman, then 30 percent of your sample would be drawn f... |
and Levels of Measurement 21. 13.2 1.4: Experimental Design and Ethics 22. A. population: all college students B. sample: the 100 college students in the study C. experimental units: each individual college student who participated D. explanatory variable: the size of the tableware E. F. treatment: tableware that is 2... |
. This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Appendix B 841 Stem Leaf 10 0 0 Table B4 29. Most scores on this exam were in the range of 70–89, with a few scoring in the 60–69 range, and a few in the 90–100 range. 2.2: Histograms, Frequency Polygons, and Time Series Graphs 30. RF = 7... |
. 46. 61.5, or $61,500 47. 49.25, or $49,250 48. The median, because the mean is distorted by the high value of one house. 2.6: Skewness and the Mean, Median, and Mode 49. C Appendix B 842 50. A 51. They will all be fairly close to one another. 2.7: Measures of the Spread of the Data 52. Mean: 15 Standard deviation: 4.... |
2 Study less than 15 hours/week 125 Total Table B5 607 200 193 393 682 318 1,000 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Appendix B 843 66. P(honor roll|study at least 15 hours word per week) = 482 1,000 = 0.482 67. P(study less than 15 hours word per week) = 125 + 193 1,000 = 0.... |
of one day, with the following result: x P(x) 0 1 2 3 4 0.20 0.45 0.20 0.10 0.05 Table B6 7. Define the random variable X for this example. 8. What is P(x > 2)? 9. What is the probability a patron will check out at least one book? 10. What is the probability a patron will take out no more than three books? 11. If the ... |
10 times he comes to bat (an at-bat), four of those times he gets a hit. You decide to track his batting performance for his next 20 at-bats. 24. Define the random variable X in this experiment. 25. Assuming Joe’s probability of getting a hit is independent and identical across all 20 at-bats, describe the distributio... |
modeled by the Poisson distribution. 38. If X = the number of drivers, and the average numbers of drivers per hour is four, how would you express this distribution? 39. What is the domain of X? 40. What are the mean and standard deviation of X? 846 Appendix B 5.1: Continuous Probability Functions 41. You conduct a sur... |
the mean and standard deviation for the distribution? 54. Write the probability density function for a variable distributed as X ~ Exp(0.2). 6.1: The Standard Normal Distribution 55. Translate this statement about the distribution of a random variable X into words: X ~ (100, 15). 56. If the variable X has the standard... |
if you conduct a study by flipping 30 coins and recording the number of heads, and repeat this 100 times, the distribution of the mean number of heads will be approximately normal. How is this possible? 69. The mean of a normally-distributed population is 50, and the standard deviation is four. If you draw 100 samples... |
and to sums of a random variable, are similar. 83. If you repeatedly draw samples of size 50 from a population with a mean of 80 and a standard deviation of four, and calculate the sum of each sample, what is the expected distribution of these sums? Use the following information to answer the next four exercises. You ... |
Z includes only positive numbers (you cannot spend a negative amount of money). Possibly the value –7 is a data entry error, or a special code to indicate that the student did not answer the question. 6. The probabilities must sum to 1.0, and the probabilities of each event must be between 0 and 1, inclusive. 7. Let X... |
, because there are not a fixed number of trials 21. X ~ B(100, 0.65) 22. μ = np = 100(0.65) = 65 23. σ x = npq = 100(0.65)(0.35) = 4.77 24. X = Joe gets a hit in one at-bat (in one occasion of his coming to bat) 25. X ~ B(20, 0.4) 26. μ = np = 20(0.4) = 8 27. σ x = npq = 20(0.40)(0.60) = 2.19 4.4: Geometric Distributi... |
) 39. The domain of X = {0, 1, 2, 3,...}; i.e., any integer from 0 upwards. 40.1: Continuous Probability Functions 41. The discrete variables are the number of books purchased, and the number of books sold after the end of the semester. The continuous variables are the amount of money spent for the books, and the amoun... |
Normal Distribution 55. The random variable X has a normal distribution with a mean of 100 and a standard deviation of 15. 56. X ~ N(0,1) This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Appendix B 851 57. z = 58 so z = 112 − 109 4.5 = 0.67 so z = 100 − 109 4.5 = − 2.00 59. z = 105 − 109... |
which the samples were drawn. 69. You would not expect each sample to have a mean of 50, because of sampling variability. However, you would expect the sampling distribution of the sample means to cluster around 50, with an approximately normal distribution, so that values close to 50 are more common than values furth... |
this is a narrower interval due to the increased sample size. 100 7.2: The Central Limit Theorem for Sums 81. For a random variable X, the random variable ΣX will tend to become normally distributed as the size n of the samples used to compute the sum increases. 82. Both rules state that the distribution of a quantity... |
σ x n ⎞ ⎠ and the standard deviation of a uniform distribution is b − a 12. In this example, the standard deviation of the distribution is b − a 12 = 0.10 12 = 0.03 ¯ so X ∼ N(0.15, 0.003) 92. ΣX ∼ N((n)(μ x), ( n)(σ x)) so ΣX ∼ N(9.0, 0.23) This OpenStax book is available for free at http://cnx.org/content/col30309/1... |
You collect data from a random sample of 20 healthy adults and find that your sample temperatures have a mean of 98.4 and a sample standard deviation of 0.3 (both in degrees Fahrenheit). 11. What are the degrees of freedom (df) for this study? 12. For a two-tailed 95 percent confidence interval, what is the appropriat... |
in a particular neighborhood is lower than the city average. Write the null and alternative hypotheses to test this. 26. State the appropriate alternative hypothesis to this null hypothesis: H0: μ = 107 27. State the appropriate alternative hypothesis to this null hypothesis: H0: p < 0.25 9.2: Outcomes and the Type I ... |
of 1.5 percent. You draw a sample of 100 children from your community and check their vaccination records to see if the vaccination rate in your community is the same as the national average. What distribution will you use for this test, and why? 9.4: Rare Events, the Sample, Decision, and Conclusion 40. You are condu... |
100 and find that 75 percent own cars. 50. What are the null and alternative hypotheses for this study? 51. What test will you use, and why? 10.1: Comparing Two Independent Population Means with Unknown Population Standard Deviations 52. You conduct a poll of political opinions, interviewing both members of 50 married... |
59. What is the random variable for this study? 60. What are the null and alternative hypotheses for this study? 61. If the 50 science students spent an average of $530 with a sample standard deviation of $20, and the 50 humanities students spent an average of $380 with a sample standard deviation of $15, would you no... |
program in improving running speed? What is the conclusion? 71. What would it mean if the t statistic had been 4.56, and what would have been your decision in that case? 11.1: Facts About the Chi-Square Distribution 72. What is the mean and standard deviation for a chi-square distribution with 20 degrees of freedom? 1... |
is your decision regarding the null hypothesis? 11.4: Test of Homogeneity 83. You conduct a chi-square test of homogeneity for data in a five-by-two table. What are the degrees of freedom for this test? 11.5: Comparison Summary of the Chi-Square Tests: Goodness-of-Fit, Independence and Homogeneity 84. A 2013 poll in t... |
function ZInterval answer is (40.78, 41.23). Answers differ due to rounding. 7. The standard error of measurement is σ n = 4 50 = 0.57 EBM = 1.96)(0.57) = 1.12 The 95 percent confidence interval is 41 ± 1.12 = (39.88, 42.12). The calculator function ZInterval answer is (40.84, 41.16). Answers differ due to rounding. 8... |
t ⎛ ⎝ s n ⎛ ⎞ ⎠ = (2.045) ⎝ ⎞ ⎠ = 0.112 0.3 30 98.4 ± 0.11 = (98.29, 98.51). The calculator function TInterval answer is (98.29, 98.51). 8.3: Confidence Interval for a Population Proportion 16. p′ = 280 500 = 0.56 q′ = 1 − p′ = 1 − 0.56 = 0.44 s = pq n = 0.56(0.44) 500 = 0.0222 17. Because you are using the normal appr... |
q EBP2 = = 0.9220 0.0016 = 576.24 22. n = 1.962 (0.5)(0.5) 0.032 You need 1,068 subjects (rounding upward from 1,067.11). n2 pq EBP2 = = 0.9604 0.0009 = 1067.11 9.1: Null and Alternate Hypotheses 23. H0: p = 0.58 Ha: p ≠ 0.58 24. H0: p ≥ 0.58 Ha: p < 0.58 25. H0: μ ≥ $268,000 860 Appendix B Ha: μ < $268,000 26. Ha: μ ≠... |
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