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) 229                                   15.9 265                                    15.7 357                                    15.4 482                                    15.3 532                                    14.9   What are the null and alternative​ hypotheses?   Construct a scatterplot. The linear correlation coefficient r is The test statistic t is The​ P-value is Because the​ P-value is ____ than the significance level 0.05​, there ____ 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? A. The results suggest that an increase in imported lemons causes car fatality rates to remain the same. B. The results do not suggest any​ cause-effect relationship between the two variables. C. The results suggest that imported lemons cause car fatalities. D. The results suggest that an increase in imported lemons causes in an increase in car fatality rates.

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print​ lengths, foot​ lengths, and heights of males. 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. Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male? Use a significance level of α=0.01.   Shoe Print​ (cm) 29.0 29.0 31.2 31.7 27.1   Foot Length​ (cm) 26.3 24.9 28.0 26.0 25.7   Height​ (cm) 177.5 173.1 181.1 181.6 176.9

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 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 a measured chest size can be used to predict the weight? Use a significance level of a = 0.05 Question: Determine the null and alternative hypotheses

The number of wins for a high school football team is measured for the season. When the team plays at home, it is generally believed that they will win. Comparing the location of the game and the number of wins, a correlation coefficient of −0.11 is calculated. What would this imply about the football team winning at home?  The scatter plot would closely resemble a straight line with a negative slope. The data has a strong, negative correlation, and a causal relationship exists between the team playing at home and winning. The scatter plot would closely resemble a straight line with a negative slope. The data has a strong, negative correlation, but causation cannot be determined. The scatter plot would not be represented by a line of best fit with a negative slope. There is a weak correlation between the football team playing at home and winning, and a causal relationship exists between the team playing at home and winning. There is no causation and almost no correlation between the…