Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality rates per​ 100,000 population. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates? Do the results suggest that imported lemons cause car​ fatalities? Lemon_Imports_(x) Crash_Fatality_Rate_(y) 232                                   15.9 266                                   15.6 357                                   15.5 481                                   15.3 532                                    14.8 What are the null and alternative​ hypotheses? Construct a scatterplot The linear correlation coefficient is The test statistic is The​ P-value is Because the​ P-value is ▼ less greater than the significance level 0.05​, there ▼ is not is sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α=0.05.   Do the results suggest that imported lemons cause car​ fatalities?

List two possible limitations of using a Pearson correlation coefficient.

We made a survey with the number of people in a household and the number of times they get sick throughout the year. In a household, 3 people get sick once, 4 people get sick twice, 2 people get sick three times and 1 person gets sick 4 times. 1) Give the correlation coefficient, proper interpretation of it, and explain the relevance to the topic

A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow:   Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800    Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary.         Find the equation of the least-squares regression line. (Round to two decimal places)

The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables number of years Espa spent by the student at the university and score on the first midterm have a sample correlation coefficient r of about -0.36. Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H . Aa 0, B H, :0 H : O=0 (b) Determine the type of test statistic to use. (Choose one) ▼ O

Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support Correlation Results the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that Correlation coeff, r: 0.959614 a measured chest size can be used to predict the weight? Use a significance level of = 0.05. Critical r: +0.2680855 P-value (two tailed): 0.000 Но: Р H1:P (Type integers or decimals. Do not round.) Identify the correlation coefficient, r. (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.) O A. There is one critical value at r= . B. There are two critical values at r= ± Is there sufficient evidence to support the claim that there is a linear correlation between…

Second part to this question is also what is test statistic t=

A researcher hypothesizes that there is a positive correlation between the hours spent studying and the final exam score. They collect data from 20 students and compute the Pearson correlation coefficient, r, to be 0.75. Using a significance level of 0.05, test the hypothesis that there is a significant correlation between the hours spent studying and the final exam score.

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, Fone the value of the linear correlation coefficient r, and find the p-value of r. Determine whether there is suffiencet evidence to support a claim of linear correlation between the two variables. Use a significance level of a=0.05  determine the linear correlation coefficient r  determine the null and alternative hypothesis  determine the test statistic  Determine the p value