Concept explainers
For Exercises 7.55–7.57, refer to Equations (7.1) and (7.2) on pages 315 and 316, respectively.
7.56 Heights of Starting Players. In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 142) to obtain the standard deviation of the heights of the five starting players on a men’s basketball team and also the standard deviation of
- a. Apply Equation (7.1) to compute σx for samples of sizes 1, 2, 3, 4, and 5. Compare your answers with those in Table 7.6.
- b. Use the simpler formula, Equation (7.2), to compute σx for samples of sizes 1, 2, 3, 4, and 5. Compare your answers with those in Table 7.6. Why does Equation (7.2) generally yield such poor approximations to the true values?
- c. What percentages of the population size are samples of sizes 1, 2, 3, 4, and 5?
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Introductory Statistics (10th Edition)
Additional Math Textbook Solutions
Essential Statistics
Statistical Reasoning for Everyday Life (5th Edition)
Probability and Statistics for Engineering and the Sciences
Business Analytics
Essentials of Statistics (6th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
- 10 – 11. Margaret, an archeologist, is conducting a test to determine if there is a positive linear relationship between the total height of a dinosaur and its leg length. Her random sample of 15 dinosaur total heights (in feet) and leg lengths (in feet) produced the results shown in the following TI calculator screen. Use the TI calculations in the screen shot to help you answer questions: 10 & 11. LinReg y=a+bx a=28.67845743 b=5.639892354 r=559696513 r=.7481286741 10. What would you predict for a dinosaur's total height (to 2 decimal places) in feet, if the leg length is 5.8 feet? a) 61.39 feet b) 28.68 feet c) 114.99 feet d) 61.33 feet e) 74.81 feet 11. What percent of variation in the dinosaur's total height can be accounted for by the variation in the dinosaur's leg length? a) 28.68% b) 5.64%% c) 55.97% d) 74.81% e) none of thesearrow_forwardThe 98.6 degree standard for human body temperature was derived by a German doctor in 1868. In an attempt to verify his claim, Mackowiak, Wasserman, and Levine22 took temperatures from 148 healthy peopleover a 3-day period. A data set closely matching the one in Mackowiak’s article was derived by Allen Shoemaker, and appears in the Journal of Statistics Education.23 The body temperatures for these 130 individuals are shown in the relative frequency histogram that follows. See Attachment a. Describe the shape of the distribution of temperatures.b. Are there any unusual observations? Can you think of any explanation for these?c. Locate the 98.6-degree standard on the horizontal axis of the graph. Does it appear to be near the center of the distribution?arrow_forwardA NASA deep space probe has an observed deviation from it's predicted path of 4.807 × 10 m - 10 while s² the Pioneer 10 and 11 spacecrafts have an observed m Compared to the - 10 deviation of 8.74 × 10- $² . Pioneer spacecraft's deviation, how many times greater are the deep space probe deviations? (answer is not in scientific notation) The deep space probe deviations are times more than the Pioneer spacecraft's.arrow_forward
- A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia = 63.3 yr. 1 X,=65.2 yr. 2 o, = 9.1 yr. = 7.3 yr. n1 = 120 = 150arrow_forwardQuestion 1 (10.2) Mark the mean of the dataset, the first principal component, and the second principal component. You don't have to calculate anything; just make approximate markings.arrow_forwardA relationship expert wants to know if people with higher levels of emotional intelligence (measured on an interval scale from 1–6, with higher numbers meaning more intelligence) will be better liked upon first meeting people (measured on a 1–5 interval scale, with higher numbers meaning more likable). X: Emotional Intelligence Score X: First Impression Rating 6 1 2.5 4 M=3.38 s=2.14 SS = 13.69 Y: First Impression Rating 5 1.5 3 3.5 M=3.25 s=1.44 SS = 6.25 a) Create a scatterplot of the data. b) Calculate r and r2 . c) Report results in APA style. d) What do the results mean?arrow_forward
- The authors of an article found that the speed of a prey (twips/s) and the length of a prey (twips ✕ 100) are good predictors of the time (seconds) required to catch the prey. (A twip is a measure of distance used by programmers.) Data were collected in an experiment in which subjects were asked to "catch" an animal of prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which the prey moved across the screen. The following data are consistent with summary values and a graph given in the article. Each value represents the average catch time over all subjects. The order of the various speed-length combinations was randomized for each subject. Prey Length Prey Speed Catch Time 7 20 1.11 6 20 1.20 5 20 1.24 4 20 1.40 3 20 1.50 3 40 1.41 4 40 1.35 6 40 1.31 7 40 1.28 7 80 1.40 6 60 1.39 5 80 1.40 7 100 1.42 6 100 1.42 7 120 1.69 5 80 1.49 3 80 1.41 6 100 1.49…arrow_forwardThe population P (in thousands) of a certain city from 2000 through 2014 can be modeled by P = 140.5ekt,arrow_forwardsevere storms indicate that e3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use off fxed cement piers. Suppose that a reading of 31 waves showed an average wave height of x= 16.7 feet. Previous studies of Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of 164 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land C (a) What is the level of significance? State the null and alternate hypotheses. Ho: H- 16.4 ft; H:>'16.4 ft Ho: H 16.4 ft; H1: = 16.4 ft Ho: H- 16.4 ft; H: H+ 16.4 ft (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard…arrow_forward
- Consider the model y=-2.45x+7.18 derived from data between x=4 and x=10. What value of x represents interpolation of the data?arrow_forwardA researcher collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.arrow_forwardIn 2001, the polls found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. Assume a recent poll asked 1940 American adults if they believe there was a conspiracy in the assassination and it found that 1519 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy is now lower? Test at the 6% level.P: PARAMETER What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: HYPOTHESES Fill in the correct null and alternative hypotheses: H0:H0: HA:HA: A: ASSUMPTIONS Since information was collected from each object, what conditions do we need to check? Check all that apply. n(1−pˆ)≥10n(1-p̂)≥10 n≥30n≥30 or normal population. np≥10np≥10 n(1−p)≥10n(1-p)≥10 N≥20nN≥20n σσ is known. n(pˆ)≥10n(p̂)≥10 σσ is unknown.…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman