Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 11.14, Problem 91E
To determine
Conduct a hypothesis test for testing that neither
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State the p value
A psychologist would like to examine the effects of sugar consumption on the activity level of preschool
children. Three samples of children are selected with n = 5 in each sample. One group gets no sugar, one
group gets a small dose, and the third group gets a large dose. The psychologist records the activity level
for each child. The data from this experiment are presented below.
No sugar
Small dose
Large dose
3
6.
3
3
8
1
7
G = 60
1
4
2
EX? = 298
3
4
T = 15
T = 20
T = 25
SS = 16
SS = 12
SS = 20
A) Solve for, Critical F: =
B) Do these data indicate any significant differences among the three groups?
Test with a = .05.
C) Do you reject or fail to reject Ho and why?
ABC
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:
x
1
2
3
4
5
y
15.8
17.3
14.4
19.6
20.0
Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272
(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
=
y
=
b
=
ŷ
=
+ x
(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.
(c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.)
r =
r2 =
What percentage of variation in y is…
Chapter 11 Solutions
Mathematical Statistics with Applications
Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2ECh. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5ECh. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7ECh. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9ECh. 11.3 - Suppose that we have postulated the model...
Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22ECh. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30ECh. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36ECh. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41ECh. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49ECh. 11.8 - Prob. 50ECh. 11.8 - Prob. 51ECh. 11.8 - Prob. 52ECh. 11.8 - Prob. 54ECh. 11.8 - Prob. 55ECh. 11.8 - Prob. 57ECh. 11.8 - Prob. 58ECh. 11.8 - Prob. 59ECh. 11.8 - Prob. 60ECh. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62ECh. 11.9 - Prob. 63ECh. 11.9 - Prob. 64ECh. 11.9 - Prob. 65ECh. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67ECh. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72ECh. 11.12 - Prob. 73ECh. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75ECh. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77ECh. 11.13 - Prob. 78ECh. 11.13 - Prob. 79ECh. 11.14 - Prob. 80ECh. 11.14 - Prob. 81ECh. 11.14 - Prob. 82ECh. 11.14 - Prob. 83ECh. 11.14 - Prob. 84ECh. 11.14 - Prob. 85ECh. 11.14 - Prob. 86ECh. 11.14 - Prob. 87ECh. 11.14 - Prob. 88ECh. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90ECh. 11.14 - Prob. 91ECh. 11.14 - Prob. 92ECh. 11.14 - Prob. 93ECh. 11.14 - Prob. 94ECh. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SECh. 11 - Prob. 98SECh. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 102SECh. 11 - Prob. 103SECh. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SECh. 11 - Prob. 106SECh. 11 - Prob. 107SE
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- Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardBighorn 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: 1. 3 4 12.2 17.5 14.4 19.6 20.0 A USE SALT Ex = 15; Ey = 83.7; Ex² = 55; Ey? = 1,446.61; Exy = 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.) y = (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y y 22 22 20 20 18 18 16 16 14 14 12 12arrow_forward
- 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: x 1 2 3 4 5 y 12.2 17.5 14.4 19.6 20.0 (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = ? r2 = ? What percentage of variation in y is explained by the least-squares model? __________ %(Round your answer to one decimal place.) incorrect answers: I submitted this question and was told this is the answer but it is NOT CORRECT. please help !! r=0.800 r2= 0.640 64% ( above answers are incorrect)arrow_forward3.24 An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213–216) describes several experiments investigating the rodding of concrete to remove entrapped air. A 3-inch × 6-inch cylinder was used, and the number of times this rod was used is the design variable. The resulting compressive strength of the concrete specimen is the response. The data are shown in the following table: Rodding Level Compressive Strength 10 1530 1530 1440 15 1610 1650 1500 20 1560 1730 1530 25 1500 1490 1510 Refer to the data above. Construct the ANOVA table manually. Show your calculation to find a. SSTotal b. SSTreatment c. SSError d. Degree of freedom e. Mean square error f. F statisticsarrow_forwardBighorn 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: x 1 2 3 4 5 y 12.2 20.9 14.4 19.6 20.0 Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6 (a) Draw a scatter diagram. (b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = + x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = Explain what these measures mean in the context of the problem. The correlation coefficient r measures the strength of the linear relationship between a bighorn sheep's age and the mortality rate. The coefficient of determination r2 measures the explained…arrow_forward
- 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: x 1 2 3 4 5 y 12.2 20.9 14.4 19.6 20.0 Σx = 15; Σy = 87.1 ; Σx2 = 55; Σy2 =1577.17; Σxy = 275.6 d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t = e) Find or estimate the P-value of the test statistic. P-value > 0.250 0.125 < P-value < 0.250 0.100 < P-value < 0.125 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 0.0005 < P-value < 0.005 P-value < 0.0005 Conclusion Reject the…arrow_forwardA 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_forwardSuppose you are interested in seeing whether the total number of days students are absent from high school correlates with their grades. You obtain school records that list the total absences and average grades (on a percentage scale) for 80 graduating seniors. You decide to use the computational formula to calculate the Pearson correlation between the total number of absences and average grades. To do so, you call the total number of absences X and the average grades Y. Then, you add up your data values (ZX and EY), add up the squares of your data values (EX² and ΣY²), and add up the products of your data values (ΣXY). The following table summarizes your results: ΣΧ 380 ΣΥ 5,820 ⠀ ΣΧ2 2,708 ΣΥ2 440,838 ΣΧΥ 26,709 The sum of squares for the total number of absences is SSx = The sum of squares for average grades is SSy = The sum of products for the total number of absences and average grades is SP = The Pearson correlation coefficient is r = Suppose you want to predict average grades…arrow_forward
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