Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find t

vazelinahS 2020-11-08 Answered
Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α=0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities? Lemon Imports230265358480530Crashe Fatality Rate15.915.715.415.314.9
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Obiajulu
Answered 2020-11-09 Author has 98 answers

Step 1 Note: we are using MINTAB software to perform the calculations. The data shows that the weights of lemon imports from Mexico and U.S. car fatality rates. The level of significance is \(\alpha = 0.05\). Procedure to obtain scatterplot using the MINITAB software: Choose Graph > Scatterplot. Choose Simple and then click OK. Under Y variables, enter a column of CRASH FERTILITY RATES. Under X variables, enter a column of LEMON IMPORTS. Click OK. Step 2 The hypotheses are given below: Null hypothesis: \(H0:\rho = 0\) That is, there is no linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates. Alternative hypothesis: \(H1:\rho\ cancel= 0\) That is, there is a linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates. Correlation coefficient r: Software Procedure: Step-by-step procedure to obtain the ‘correlation coefficient’ using the MINITAB software: Select Stat >Basic Statistics > Correlation. In Variables, select LEMON IMPORTS and CRASH FERTILITY RATES from the box on the left. Click OK. Output using the MINITAB software is given below: Correlations: LEMON IMPORTS, CRASH FATALITY RATE Pearson correlation of LEMON IMPORTS and CRASH FATALITY RATE \(= -0.959\)
\(P-value = 0.010\) Step 3 Thus, the Pearson correlation of weights of lemon imports from Mexico and U.S. car fatality rates is –0.959 and the P-value is 0.010. Critical value: From the TABLE “Critical Values of the Pearson Correlation Coefficient r”, the critical value for 5 degrees of freedom for \(\alpha = 0.05\) level of significance is \(\pm 0.878\). The horizontal axis represents weights of lemon imports from Mexico and vertical axis represents U.S. car fatality rates. From the plot, it is observed that there is a linear association between the weights of lemon imports from Mexico and U.S. car fatality rates because the data point show a distinct pattern. The P-value is 0.010 and the level of significance is 0.05. Here, the P-value is less than the level of significance. Hence, the null hypothesis is rejected. That is, there is a linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates. The critical value is \(\pm 0.878\). Here, the correlation value –0.959 lies beyond the lower critical value. Thus, there is sufficient evidence to support the claim that there is a linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates. There is a linear correlation between the weights of lemon imports from Mexico and U.S. car fatality rates but it does not appear the imported lemons cause car fatalities because, it do not suggest any cause-effect relationship.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-20
The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the mean and variance of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?
asked 2021-03-07
A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point (4, 5). Write an equation that represents the path.
asked 2021-02-25
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. (1,3),(2,6),(3,12),(4,24)
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.
asked 2021-01-06
A weather forecaster predicts that the temperature in Antarctica will decrease 8F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36F
asked 2021-02-12
The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.
Movie A: y=x2+35x+100
Movie B: y=5x+275
Where x is number of days since the movies opened.
When is the attendance for each movie the same?
asked 2020-11-12
What is a data model, and why is its purpose? What is conceptual modeling? What do we need to use conceptual modeling? What are the functions of a DBMS? Provide an example of their use.
asked 2021-10-27
Which of the following is nota condition for constructing a confidence interval to estimate the difference between two population proportions?
A. The samples must be selected randomly.
B. The data must come from populations with approximately normal distributions.
C. When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample.
D. The samples must be independent of each other.
E. The observed number of successes and failures for both samples must be at least 10.