Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 6.5, Problem 48E
To determine
Find the probability density
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were:
Student
High School GPA
Freshmen GPA
1
2.0
1.6
2
2.2
2.0
3
2.6
1.8
4
2.7
2.8
5
2.8
2.1
6
3.1
2.0
7
2.9
2.6
8
3.2
2.2
9
3.3
2.6
10
3.6
3.0
We would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4.
Provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!).
a) What would be your approximate 95% prediction interval for question (g)?
b) Show your scatterplot with the predicted trend line below
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Full data set
Car 1
216
243
205
242
239
297
295
172
270
251
165
310
265
316
278
Car 2
231
220
223
205
245
257
242
292
248
252
287
255
250
293
251
.....
Describe each data set, that is determine the shape, center, and spread.
Sample mean for Car 1
x=__________mi / 10 gal
(Type an integer or decimal rounded to one decimal place as needed.)
Sample mean for Car 2
x=___________mi / 10 gal
(Type an integer or decimal rounded to one decimal place as needed.)
Median for Car 1
M=____________mi / 10 gal
(Type an integer or decimal rounded to one decimal place as needed.)
Median for Car 2
M=___________mi / 10 gal
(Type…
1. A researcher observed a rat respond for a food reward by pressing one of the three levers in a cage. Pressing the lever to the right (R) produced no food reward. pressing the lever to the left (L) produced a single food pellet, and pressing the lever at the center (C) produced two food pellets. Because the center level produced the largest reward, the researcher hypothesized that the rat would press this lever most often. Each trial ended when the rat produced a level. The researcher recorded lever pressing for 30 trials.
L, L, R, L, R, C, R, L, C, L,
L, C, C, C, R, C, R, C, L, C,
C, L, C, C, C, L, C, C, C, C, C
- Create the appropiate graph for this data
- Do these data support the hypothesis? Explain.
2. Which scales of measurement are assumed to be discrete? What does this mean? Which scales of measurement are assumed to be continuous? What does this mean?
3. What type of graph should you create to visualize the following frequency data? Explain.
-…
Chapter 6 Solutions
Mathematical Statistics with Applications
Ch. 6.3 - Let Y be a random variable with probability...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - The amount of flour used per day by a bakery is a...Ch. 6.3 - Prob. 5ECh. 6.3 - The joint distribution of amount of pollutant...Ch. 6.3 - Suppose that Z has a standard normal distribution....Ch. 6.3 - Assume that Y has a beta distribution with...Ch. 6.3 - Prob. 9ECh. 6.3 - The total time from arrival to completion of...
Ch. 6.3 - Suppose that two electronic components in the...Ch. 6.3 - Prob. 12ECh. 6.3 - If Y1 and Y2 are independent exponential random...Ch. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - A member of the Pareto family of distributions...Ch. 6.3 - Prob. 19ECh. 6.3 - Let the random variable Y possess a uniform...Ch. 6.3 - Prob. 21ECh. 6.4 - Prob. 23ECh. 6.4 - In Exercise 6.4, we considered a random variable Y...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Let Y have a uniform (0, 1) distribution. Show...Ch. 6.4 - Prob. 29ECh. 6.4 - A fluctuating electric current I may be considered...Ch. 6.4 - The joint distribution for the length of life of...Ch. 6.4 - Prob. 32ECh. 6.4 - The proportion of impurities in certain ore...Ch. 6.4 - A density function sometimes used by engineers to...Ch. 6.4 - Prob. 35ECh. 6.4 - Refer to Exercise 6.34. Let Y1 and Y2 be...Ch. 6.5 - Let Y1, Y2,, Yn be independent and identically...Ch. 6.5 - Let Y1 and Y2 be independent random variables with...Ch. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - A type of elevator has a maximum weight capacity...Ch. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - The manager of a construction job needs to figure...Ch. 6.5 - Suppose that Y has a gamma distribution with =...Ch. 6.5 - A random variable Y has a gamma distribution with ...Ch. 6.5 - Prob. 48ECh. 6.5 - Let Y1 be a binomial random variable with n1...Ch. 6.5 - Let Y be a binomial random variable with n trials...Ch. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Let Y1,Y2,,Yn be independent binomial random...Ch. 6.5 - Prob. 54ECh. 6.5 - Customers arrive at a department store checkout...Ch. 6.5 - The length of time necessary to tune up a car is...Ch. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.6 - In Example 6.14, Y1 and Y2 were independent...Ch. 6.6 - Refer to Exercise 6.63 and Example 6.14. Suppose...Ch. 6.6 - Prob. 65ECh. 6.6 - Prob. 66ECh. 6.6 - Prob. 67ECh. 6.6 - Prob. 68ECh. 6.6 - Prob. 71ECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - As in Exercise 6.72, let Y1 and Y2 be independent...Ch. 6 - Let Y1, Y2,, Yn be independent, uniformly...Ch. 6 - Prob. 75SECh. 6 - Prob. 76SECh. 6 - Prob. 77SECh. 6 - Prob. 78SECh. 6 - Refer to Exercise 6.77. If Y1,Y2,,Yn are...Ch. 6 - Prob. 80SECh. 6 - Let Y1, Y2,, Yn be independent, exponentially...Ch. 6 - Prob. 82SECh. 6 - Prob. 83SECh. 6 - Prob. 84SECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - Prob. 86SECh. 6 - Prob. 87SECh. 6 - Prob. 88SECh. 6 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 6 - Prob. 90SECh. 6 - Prob. 91SECh. 6 - Prob. 92SECh. 6 - Prob. 93SECh. 6 - Prob. 94SECh. 6 - Prob. 96SECh. 6 - Prob. 97SECh. 6 - Prob. 98SECh. 6 - Prob. 99SECh. 6 - The time until failure of an electronic device has...Ch. 6 - Prob. 101SECh. 6 - Prob. 103SECh. 6 - Prob. 104SECh. 6 - Prob. 105SECh. 6 - Prob. 106SECh. 6 - Prob. 107SECh. 6 - Prob. 108SECh. 6 - Prob. 109SECh. 6 - Prob. 110SECh. 6 - Prob. 111SECh. 6 - Prob. 112SECh. 6 - Prob. 113SECh. 6 - Prob. 114SECh. 6 - Prob. 115SECh. 6 - Prob. 116SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- A study conducted at Ateneo de Naga University revealed that students who attended class 95 to 100% of the time usually received an A in the class. Students who attended class 80 to 90% of the time usually received a C+ to B+ in the class. Students who attended class less than 80% of the time usually received a D or an F or eventually withdrew from the class. In this research in AdNU with 5000 students in which 100 students participated in the survey, what is the parameter of the study? a. 80% b. 80 - 90% c. 100 d. 95 - 100 % e. 5000arrow_forwardAt a shooting range, instructors can determine if a shooter is consistently missing the target because of the gun sight or because of the shooter's ability. If a gun's sight is off, the variance of the distances between the shots and the center of the shot pattern will be small (even if the shots are not in the center of the target). A student claims that it is the sight that is off, not his aim, and wants the instructor to confirm his claim. If a skilled shooter fires a gun at a target multiple times, the distances between the shots and the center of the shot pattern, measured in centimeters (cm), will have a variance of less than 0.32. After the student shoots 26 shots at the target, the instructor calculates that the distances between his shots and the center of the shot pattern, measured in cmcm, have a variance of 0.18. Does this evidence support the student’s claim that the gun’s sight is off? Use a 0.005 level of significance. Assume that the distances between the shots and the…arrow_forwardA panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in the study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. To test for significance of their findings, which of the following should the dentists use? Select one: a.Paired t-test b.One-sample t-test for a mean c.Linear Regression d.One-sample Z-test for a proportion e.Chi-Square test for independence f.Two-Sample t-test g.One-sample Z-test for a meanarrow_forward
- A panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in this study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. ******In the sample, 6 of the 30 patients assigned to Brand A were found to have a cavity. The fraction 6/30 should be denoted by which of the following? μ x̄ p p̂ n s σ χ²arrow_forwardIn the Chernobyl nuclear accident it is estimated that 30,000 people received an average dose of 45 REM. For this population, using the linear hypothesis, how many "normal" deaths from cancer are expected and how many additional deaths from the radiation of the accident? Group of answer choices 500 normal, 6000 additional 1000 normal, 4000 additional 2000 normal, 3000 additional 4000 normal, 1000 additional 6000 normal, 500 additionalarrow_forward2- An expert estimates that the distribution parameter for durability times of parts produced with machine A in the factory is different from the distribution parameter for durability times of parts produced with machine B. Durability times of 4 parts produced from machine A and 4 parts produced from machine B are given below. Find the Mann-Whitney U value by using these data. a) 18 B) 6 NS) 16 D) 20 TO) 12arrow_forward
- Section 11.2 Question #9 In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 278 kicks during games among top teams. In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks? View the penalty kick data. Pentalty kick data Dialog content starts Goalkeeper Jump Left Center Right Kick to Left 54 0 36 Kick to Center 41 10 28 Kick to Right 41 6 62 Determine the test statistic. χ2=____________(Round to three…arrow_forwardWhen random samples are drawn so that the selection of a case for one sample has no effect on the selection of cases for another sample, the samples are A. Dependent B. Independent C. Simple D. Systemoarrow_forwardUse this data and create a model that estimates a student's giving rate as an alumni based on the three parameters provided. If a class has a graduation rate of 74, the % of classes under 20 student equal to 55, and a Student=Faculty Ratio of 19, what should we expect our Alumni Giving Rate to be? (Enter a whole number) University Graduation Rate % of Classes Under 20 Student-Faculty Ratio Alumni Giving Rate Boston College 85 39 13 25 Brandeis University 79 68 8 33 Brown University 93 60 8 40 California Institute of Technology 85 65 3 46 Carnegie Mellon University 75 67 10 28 Case Western Reserve Univ. 72 52 8 31 College of William and Mary 89 45 12 27 Columbia University 90 69 7 31 Cornell University 91 72 13 35 Dartmouth College 94 61 10 53 Duke University 92 68 8 45 Emory University 84 65 7 37 Georgetown University 91 54 10 29 Harvard University 97 73 8 46 Johns Hopkins University 89 64 9 27 Lehigh University 81 55 11 40 Massachusetts Inst.…arrow_forward
- A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fifteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past12 months. Her data are given below, with x denoting the earnings per share from the previous year and y denoting the current stock price (both in dollars). A scatter plot of her data is shown in Figure 1. Also given is the product of the earnings per share and the current stock price for each of the fifteen stocks. (These products, written in the column labelled " xy Earnings per share, x (in dollars) Current stock price, y (in dollars) xy 49.65 1.53 75.9645 27.34 1.09 29.8006 36.07 1.47 53.0229 21.11 0.70 14.777 58.19 2.32 135.0008 58.32 2.86 166.7952 43.48 1.08 46.9584 18.20 0.85 15.47 41.85 1.68 70.308 32.39 1.68 54.4152 30.67 1.34 41.0978 42.03 1.54 64.7262 15.56 0.54 8.4024…arrow_forwardNeed help with parts d and k. Data: TSERofReturn AcmeRofReturn 1 0.42478 -0.48194 2 1.61213 -0.73284 3 -0.98754 -2.28445 4 -0.30013 -1.55312 5 1.41215 0.68674 6 0.68725 -1.31132 7 0.03733 -0.83295 8 -1.72494 -1.71975 9 0.33729 1.14443 10 -1.07502 -1.79885 11 0.86222 0.89736 12 1.17468 1.66664 13 -0.38761 -0.02658 14 1.66212 0.9086 15 1.09969 1.99935 16 -0.06266 0.46148 17 -1.96241 -1.41004 18 -1.32499 -0.38086 19 -1.51247 -1.90904 20 0.74974 0.91873 21 -0.38761 -0.49714 22 -0.17514 -1.31385 23 -3.41222 -1.15681 24 -0.01266 2.11718 25 0.16231 1.78766 26 -0.82506 1.30344 27 -0.41261 -0.43377 28 0.2623 -1.70274 29 -1.16251 0.4692 30 -1.05003 0.27671 31 -0.65008 -0.63741 32 0.62475 2.9895 33 -0.68758 1.3613 34…arrow_forwardA professional golfer is shopping for a new brand of golf ball. She likes most of the features of one particular brand, but she wants to make sure that the brand has a desirable spin rate (the rate at which the ball spins on its axis after being struck by a golf club). To test the spin rate of this new brand of ball, the golfer hits the brand of ball on 76 shots, and a computer measures the spin rate for each shot. The computer then produces the following histogram summarizing the 76 spin rates. 25 20 15 10 5 0 Frequency 4 12 13 22 19 6 5000 5500 6000 6500 7000 7500 8000 Spin rate (in revolutions per minute) Based on the histogram, estimate the mean spin rate (in revolutions per minute) for the sample. Carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License