A random sample of two variables, x and y, produced the following observations: Develop a scatter plot for the two variables and describe what relationship, if any, exists. Compute the correlation coefficient for these sample data. Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test x y 3.0 1.5 2.0 0.5 2.5 1.0 3.0 1.8 2.5 1.2 4.0 2.2 1.5 0.4 1.0 0.3 2.0 1.3 2.5 1.0

A random sample of two variables, x and y, produced the following observations: Develop a scatter plot for the two variables and describe what relationship, if any, exists. Compute the correlation coefficient for these sample data. Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test x y 3.0 1.5 2.0 0.5 2.5 1.0 3.0 1.8 2.5 1.2 4.0 2.2 1.5 0.4 1.0 0.3 2.0 1.3 2.5 1.0

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a =0.05. Internet Users 79.9 79.4 55.8 67.9 77.3 39.0 Award Winners 5.4 9.1 3.4 1.8 10.6 0.1 Construct a scatterplot. Choose the correct graph below. O A. В. C. D. 12- 12- 12- 12- 0+ 30 0+ 30 0- 30 90 90 30 90 90 Internet Users Internet Users Internet Users Internet Users The linear correlation coefficient is r= (Round to three decimal places as needed.)
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. Internet Users 80.1 78.1 57.2 66.4 76.9 38.6 O Award Winners 5.3 9.4 3.3 1.8 10.7 0.1
You wish to determine if there is a negative correlation between the two variables at a significance level of a = 0.05. You have the following data set: y 22.1 43.8 24.9 37.2 25.4 33.4 32.5 42.3 23.3 56.5 22.6 54.7 28.9 25.2 What is the correlation coefficient for this data set? Round to 3 decimal places Find the test statistic, p-value, df, and critical value(s) for a Correlationt Test on this data. Round to 3 decimal places t = p-value = %3D df = tc = Your final conclusion is that... OThere is not enough evidence to show that there is a negative correlation between the two variables. There is enough evidence to show that there is a negative correlation between the two variables.
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01. Internet Users 78.1 80.6 56.3 66.2 77.1 38.5 Award Winners 5.7 8.9 3.4 1.7 10.6 0.1
The Minitab output shown below was obtained by using paired data consisting of weights (in Ib) of 27 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 4500 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 27 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Click the icon to view the Minitab display. Minitab output The linear correlation coefficient is. (Round to three decimal places as needed.) The regression equation is Highway = 50.4- 0.00535 Weight %3D Predictor Сoef SE Coef T Constant 50.383 2.732 17.75 0.000 Weight - 0.0053502 0.0007856 -7.55 0.000 S= 2.17876 R-Sq = 65.1% R-…
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A study was done to look at the relationship between number of partners college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Partners 7 8 6 1 6 6 4 GPA 1.4 1.5 1.4 3 2.3 1.5 2.9 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are:H0:H0: ? r ρ μ Incorrect == 0 Ha:Ha: ? r ρ μ Incorrect ≠≠ 0 Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. You may want to reference the 95% Critical Values of the Sample Correlation Coefficient. There is statistically insignificant evidence to conclude that there is a correlation between the number of partners students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a student who has had more partners will have a lower GPA than a…
Match the following sample correlation coefficients with the explanation of what that correlation coefficient means. Type the correct letter in each box. 1. r= 1 2. r = -1 3. r=-.15 4. r = .1 A. a weak positive relationship between x and y B. a weak negative relationship between x and y C. a perfect negative relationship between x and y D. a perfect positive relationship between x and y
A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAS. The results of the survey are shown below. Lovers GPA 6 3 4 4 7 6 2.2 2.2 2.3 2 2 3.4 3.8 1.9 2.3 a. Find the correlation coefficient: r= Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: Hj: ?v + 0 = 0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in…
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α = 0.05. Internet Users Award Winners O A. Award Winners 12- 0- 30 Internet Users 90 81.0 5.6 Q 79.2 56.8 8.8 3.4 The linear correlation coefficient is r = (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: P H₁: p (Type integers or decimals. Do not round.) The test statistic is t = (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) 67.1 1.7 OB. Award Winners 12- 0- 30 Because the P-value of the linear correlation coefficient is Internet users and scientific award winners. 76.9 37.7 10.5 0.1 Internet Users…
For which of these research situations would you most likely calculate a Pearson's r correlation coefficient? independent variable = age; dependent variable = memory test score independent variable = type of car owned; dependent variable = money spent on gasoline per week independent variable = college major; dependent variable = GPA independent variable = city of residence; dependent variable = miles driven per week
Suppose we have the following paired observations of variables X and Y: X Y 8 0 4 10 12 20 Draw the scatter plot comparing X and Y. Calculate the values of the sample covariance and sample correlation between X and Y. Using this information, how would you characterize the relationship between X and Y ?