Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.5, Problem 49E
The accompanying summary quantities for x = Particulate pollution (μg/m3) and y = Luminance (0.01 cd/m2) were calculated from a representative sample of data that appeared in the article “Luminance and Polarization of the Sky Light at Seville (Spain) Measured in White Light” (Atmospheric Environment [1988]: 595–599).
- a. Test to see whether there is a
positive correlation between particulate pollution and luminance in the population from which the data were selected. - b. What proportion of observed variation in luminance can be attributed to the approximate linear relationship between luminance and particulate pollution?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents.
Σx = 476, Σy = 87.1, Σx2 = 62,290, Σy2 = 2046.87, Σxy = 11121.3,and r ≈ 0.94367.
x days 72 76 32 91 205y km/100 14.7 19.6 5.3 11.7 35.8
a) Use a 1% level of significance to test the claim ? > 0.(Use 2 decimal places.)t =critical t=
b) Find the predicted distance (km/100) when a drift bottle has been floating for 60 days. (Use 2 decimal places.)________ km/100
c) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.)lower limit = _____…
The article refered to in Exercise 1 also considered the effect of gypsum on the electric
conductivity (in dS m) of soil. Two types of soil were each treated with three different
amounts of gypsum, with two replicates for each soil-gypsum combination. The data are
presented in the following table.
Soil Type
Gypsum (g/kg)
Las Animas
Madera
0.00
1.52
1.05
1.01
0.92
0.27
1.49
0.91
1.12
0.92
0.46
0.9
0.92
0.88
0.92
Is there convincing evidence of an interaction between the amount of gypsum and soil
type?
Can you conclude that the conductivity differs among the soil types?
Can you conclude that the conductivity differs with the amount of gypsum added?
C.
1. Given that Y = eiax + Cosx, find:
dy
a.
dr
b. d'y/dx
2. The ages of a random sample of depositors at a named bank in Lusaka are as follows:
34
28
46
37
33
24
29
45
37
34
32
25
50
54
32
36
38
41
38
44
28
43
40
49
30
46
27
34
61
33
a. Display the data presented above on a stem and leaf display
b. State any three reasons why statisticians would display data on a stem and leaf
c. Find
i. Mean
ii. Variance
iii. Standard deviation
3. The profits to be realised from airtime vending business, to the nearest S1 000, are believed to
follow the probability distribution shown below:
-2 000
-1 000
1 000
2 000
3 000
P(X = x)
0.1
0.1
0.2
K
0.3
0.1
a. Determine the value of K.
b. Find the probability that the airtime vending
i.
Makes a loss
ii.
Realises profit of at least $2 000
c. Find
i.
The expected earnings and
Standard deviation of profits for the air time vending business
ii.
d. Is the air time vending business likely to be successful? Explain
4. In the table below, 55 students have been…
Chapter 13 Solutions
Introduction to Statistics and Data Analysis
Ch. 13.1 - Prob. 1ECh. 13.1 - The flow rate in a device used for air quality...Ch. 13.1 - The paper Predicting Yolk Height, Yolk Width,...Ch. 13.1 - Prob. 4ECh. 13.1 - Suppose that a simple linear regression model is...Ch. 13.1 - a. Explain the difference between the line y x...Ch. 13.1 - Prob. 7ECh. 13.1 - Hormone replacement therapy (HRT) is thought to...Ch. 13.1 - Prob. 9ECh. 13.1 - A simple linear regression model was used to...
Ch. 13.1 - Consider the accompanying data on x = Advertising...Ch. 13.2 - What is the difference between and b? What is the...Ch. 13.2 - The largest commercial fishing enterprise in the...Ch. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - An experiment to study the relationship between x...Ch. 13.2 - The paper The Effects of Split Keyboard Geometry...Ch. 13.2 - The authors of the paper Decreased Brain Volume in...Ch. 13.2 - Do taller adults make more money? The authors of...Ch. 13.2 - Researchers studying pleasant touch sensations...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Consider the accompanying data on x = Research and...Ch. 13.2 - Prob. 25ECh. 13.2 - In anthropological studies, an important...Ch. 13.3 - The graphs accompanying this exercise are based on...Ch. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - The article Vital Dimensions in Volume Perception:...Ch. 13.3 - Prob. 31ECh. 13.3 - An investigation of the relationship between x =...Ch. 13.4 - Prob. 33ECh. 13.4 - Prob. 34ECh. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - A subset of data read from a graph that appeared...Ch. 13.4 - Prob. 38ECh. 13.4 - Prob. 39ECh. 13.4 - Prob. 40ECh. 13.4 - The shelf life of packaged food depends on many...Ch. 13.4 - For the cereal data of the previous exercise, the...Ch. 13.4 - The article Performance Test Conducted for a Gas...Ch. 13.5 - Prob. 44ECh. 13.5 - Prob. 45ECh. 13.5 - A sample of n = 353 college faculty members was...Ch. 13.5 - Prob. 47ECh. 13.5 - Prob. 48ECh. 13.5 - The accompanying summary quantities for x =...Ch. 13.5 - Prob. 50ECh. 13.5 - Prob. 51ECh. 13.6 - Prob. 52ECh. 13 - Prob. 53CRCh. 13 - Prob. 54CRCh. 13 - Prob. 55CRCh. 13 - The article Photocharge Effects in Dye Sensitized...Ch. 13 - Prob. 57CRCh. 13 - Prob. 58CRCh. 13 - Prob. 59CRCh. 13 - Prob. 60CRCh. 13 - Prob. 61CRCh. 13 - The article Improving Fermentation Productivity...Ch. 13 - Prob. 63CRCh. 13 - Prob. 64CRCh. 13 - Prob. 65CRCh. 13 - Prob. 1CRECh. 13 - Prob. 2CRECh. 13 - Prob. 3CRECh. 13 - Prob. 4CRECh. 13 - Prob. 5CRECh. 13 - The accompanying graphical display is similar to...Ch. 13 - Prob. 7CRECh. 13 - Prob. 8CRECh. 13 - Consider the following data on y = Number of songs...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - Prob. 11CRECh. 13 - Prob. 12CRECh. 13 - Prob. 13CRECh. 13 - Prob. 14CRECh. 13 - The discharge of industrial wastewater into rivers...Ch. 13 - Many people take ginkgo supplements advertised to...Ch. 13 - It is hypothesized that when homing pigeons are...Ch. 13 - Prob. 18CRE
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
- 17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Countarrow_forwardThe standard pH of a drinking water of MRWD is pH 7.0, the pH obtained from several water station are as follows: Station 1 7.8 Station 2 6.5 Station 3 5.8 Station 4 8.9 Station 5 6.8 Station 6 5.8 Station 7 9.0 Station 8 6.9 Test the hypothesis that the drinking water of the MRWD is safe for drinking.arrow_forwardC webassign.net/web/Student/Assignment-Responses/submit?dep=30747029&tags=autosave#question4028933_1 62°F Cloudy Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: kuami b= ý = 20.0 Σχ = 15; Σy = 84.1; Σx2 = 55; Σy2 = 1,452.93; Σxy = 268.8 = (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) X 22 20 (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y 18 16 14 1 12 IOI 8 + Q Search 22 20 18 16 12 20 13 Paused Update MAX 174 11:16 PM 2/26/2023arrow_forward
- The following scatterplot shows the mean annual carbon dioxide (CO,) in parts (CO2) per million (ppm) measured at the top of a mountain and the mean annual air temperature over both land and sea across the globe, in degrees Celsius (C). Complete parts a through h on the right. f) View the accompanying scatterplot of the residuals vs. CO2. Does the scatterplot of the residuals vs. CO, show evidence of the violation of any assumptions behind the regression? 16.800 A. Yes, the outlier condition is violated. 16.725 O B. Yes, the linearity and equal variance assumptions are violated. 16.650 C. Yes, the equal variance assumption is violated. 16.575 O D. No, all assumptioris are okay. 16.500 O E. Yes, all the assumptions are violated. 325.0 337.5 350.0 362.5 CO2 (ppm) OF Yes, the linearity assumption is violated. his vear, What mean temperature doesarrow_forwardA pilot study was performed to investigate the effect of temperature, x (in degree Fahrenheit) on the electrical power consumed, y (in Watt) by an automotive factory. Other factors were kept constant and the data were collected from the study. The summary of the data are given as follows: n = 8, 2x = 401, 2301, x? = 22495 2y? = 666509, Σ > xy = 118652. %3D Compute the equation of the least squares regression line of y on x. Interpret the equation obtained in part (i). Predict the power consumption for a temperature of 65°F. (i) (ii) (iii) (iv) Compute the coefficient of determination and explain.arrow_forwardI. Solve for Z and find its area1. Mean = 81, score: x = 71.5, standard deviation: σ = 9.2. Mean = 47, score: x = 55.6, standard deviation: σ = 4.3. Mean = 68, score: x = 78.8, standard deviation: σ = 6.4. Mean = 51, score: x = 69, standard deviation: σ =7.5. Mean = 85, score: x = 93, standard deviation: σ =5.6. The mean expenses of Dela Cruz Family is PhP12,600 every 15 days and thestandard deviation is PhP 1, 570., If the expenses are normally distributed, what isthe probability of consuming less than PhP 11,000 in 15 days?7. The mean production of factory workers is 10 finished products per hour, with astandard deviation of 1.5 products/hour. What is the probability of finishing: a.less than 12.8 products/hour? b. more than 12 products/hour?8. The mean weight of insects for laboratory experiments is 13.2 g, with the standarddeviation of 0.8 g. What is the probability of randomly selecting insects withweight of : a. 14 g? b. 13.1 to 13.6 g?9. The lifetime of CP batteries from a…arrow_forward
- Like hurricanes and earthquakes, geomagnetic storms are natural hazards with possible severe impact on the Earth. Severe storms can cause communication and utility breakdowns, leading to possible blackouts. The National Oceanic and Atmospheric Administration beams electron and proton flux data in various energy ranges to various stations on the Earth to help forecast possible disturbances. The following are 25 readings of proton flux in the 47-68 kEV range (units are in p/ (cm2- sec-ster-MeV)) on the evening of December 28, 2011: 2310 2320 2010 10800 2190 3360 5640 2540 3360 11800 2010 3430 10600 3500 10200 8550 9500 2260 7730 2250 7370 2160 3200 2020 2850 (a) Find a point estimate of the mean proton flux in this time period. (b) Find a point estimate of the standard deviation of the proton flux in this time period. (c) Find an estimate of the standard error of the estimate in part (a).arrow_forwardWhat is the relationship of alpha when OA moves to OBarrow_forwardI. Solve for Z and find its area 1. Mean = 81, score: x = 71.5, standard deviation: o = 9. 2. Mean = 47, score: x = 55.6, standard deviation: o = 4. 3. Mean = 68, score: x = 78.8, standard deviation: o = 6. 4. Mean = 51, score: x = 69, standard deviation: o =7. 5. Mean = 85, score: x = 93, standard deviation: o =5. 6. The mean expenses of Dela Cruz Family is PhP12,600 every 15 days and the standard deviation is PhP 1, 570., If the expenses are normally distributed, what is the probability of consuming less than PhP 11,000 in 15 days? 7. The mean production of factory workers is 10 finished products per hour, with a standard deviation of 1.5 products/hour. What is the probability of finishing: a. less than 12.8 products/hour? b. more than 12 products/hour? 8. The mean weight of insects for laboratory experiments is 13.2 g, with the standard deviation of 0.8 g. What is the probability of randomly selecting insects with weight of: a. 14 g? b. 13.1 to 13.6 g? 9. The lifetime of CP…arrow_forward
- . Use the control variable Y = cos(X), to estimate 0 = cos xdx %3D e Provide a step-by-step explanation of your approacharrow_forwardIn an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the following table. X1 X2 y 32 20.0 28 39 23.0 28 20 12.8 32 21 16.0 29 25 10.2 31 20 11.6 28 32 17.6 25 29 17.8 28 27 16.0 29 43 26.2 27 22 9.6 32 22 15.2 32 18 8.8 43 32 20.4 24 22 12.2 36 25 14.6 36 25 10.4 29 20 11.6 30 20 12.6 31 24 16.2 36 18 9.2 34 28 16.8 30 a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. d. Which of the models in parts (a) through (c) is the best of the three? Why do you think %3D + E. so?arrow_forwardA set of data is found to have a μμ = 10 and a σσ = 2. What is σ2σ2 for this data set? Suppose each data value was divided by 5. What is μμ of the resulting data set? What is σσ of the resulting data set? What is σ2σ2 of the resulting data set?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY