# Lemons and Car Crashes Listed below are annual data for various years. The data are weigh

Question
Modeling

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? $$\begin{array}{|c|c|}Lemon\ imports &230&265&368&480&630\\ Crash\ Fatality\ Rate&159&157&15.3&15.4&14.9\end{array}$$

2021-02-25
Step 1 The null and alternative hypotheses are, $$H_0 : p = 0$$ There is no significance difference between weight of lemon imports from Mexico and U.S. car fatality rate. $$H_a : p \neq 40$$ There is a difference between weight of lemon imports from Mexico and U.S. car fatality rate. This is a two-tailed test.The linear correlation coefficient is obtained using the Excel function = CORREL(array1, array2) results is – 0.959.

### Relevant Questions

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 $$\alpha = 0.05$$. 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? $$\begin{matrix} \text{Lemon Imports} & 230 & 265 & 358 & 480 & 530\\ \text{Crashe Fatality Rate} & 15.9 & 15.7 & 15.4 & 15.3 & 14.9\\ \end{matrix}$$

Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \\ \hline \end{array}$$

b) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \\ \hline \end{array}$$

c) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \\ \hline \end{array}$$

d) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \\ \hline \end{array}$$

You just bought a new car for \$22,000. Assume that the value of your new car depreciates at a constant $$12\ \%$$ per year.

1) The decay rate is square

2) The decay factor is square

3) The equation of the function that represents the value, V(t), of the car in dollars t years from now is $$V\ =\ \Box$$ (Write an expression that completes the function's equation.)

The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city. $$\begin{array}{|c|c|} \hline Population\ (thousands) & Walking Speed\ (feet\ per\ second) \\ \hline 5.5 & 0.6 \\ \hline 14 & 1.0\\ \hline 71 & 1.6\\ \hline 138 & 1.9\\ \hline 342 & 2.2\\ \hline \end{array}$$

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

$$\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}$$

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

$$\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}$$

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

The tables show the battery lives (in hours) of two brands of laptops. a) Make a double box-and-whisker plot that represent's the data. b) Identifity the shape of each distribution. c) Which brand's battery lives are more spread out? Explain. d) Compare the distributions using their shapes and appropriate measures of center and variation.

An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
$$\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 20 & 38 & 28 \\ \hline No\ hypertension & 50 & 27 & 18 \\ \hline \end{array}$$
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.

An analysis of laboratory data collected with the goal of modeling the weight (in grams) of a bacterial culture after several hours of growth produced the least squares regression line $$\log(weight) = 0.25 + 0.61$$hours. Estimate the weight of the culture after 3 hours.

A) 0.32 g

B) 2.08 g

C) 8.0 g

D) 67.9 g

E) 120.2 g

Gastroenterology
We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.
If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?
Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?
Relationship between protein concentration $$(mg/mL)$$ of duodenal secretions to pancreatic function as measured by trypsin secretion:
$$[U/ \frac{kg}{hr}]$$
Tapsin secreton [UGA]
$$\leq\ 50$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.7 \\ \hline 2 & 2.0 \\ \hline 3 & 2.0 \\ \hline 4 & 2.2 \\ \hline 5 & 4.0 \\ \hline 6 & 4.0 \\ \hline 7 & 5.0 \\ \hline 8 & 6.7 \\ \hline 9 & 7.8 \\ \hline \end{array}$$
$$51\ -\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}$$
$$>\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 2.9 \\ \hline 2 & 3.8 \\ \hline 3 & 4.4 \\ \hline 4 & 4.7 \\ \hline 5 & 5.5 \\ \hline 6 & 5.6 \\ \hline 7 & 7.4 \\ \hline 8 & 9.4 \\ \hline 9 & 10.3 \\ \hline \end{array}$$

The article “Stochastic Modeling for Pavement Warranty Cost Estimation” (J. of Constr. Engr. and Mgmnt., 2009: 352–359) proposes the following model for the distribution of Y = time to pavement failure. Let $$\displaystyle{X}_{{{1}}}$$ be the time to failure due to rutting, and $$\displaystyle{X}_{{{2}}}$$ be the time to failure due to transverse cracking, these two rvs are assumed independent. Then $$\displaystyle{Y}=\min{\left({X}_{{{1}}},{X}_{{{2}}}\right)}$$. The probability of failure due to either one of these distress modes is assumed to be an increasing function of time t. After making certain distributional assumptions, the following form of the cdf for each mode is obtained: $$\displaystyle\Phi{\left[\frac{{{a}+{b}{t}}}{{\left({c}+{\left.{d}{t}\right.}+{e}{t}^{{{2}}}\right)}^{{\frac{{1}}{{2}}}}}\right]}$$ where $$\Uparrow \Phi$$ is the standard normal cdf. Values of the five parameters a, b, c, d, and e are -25.49, 1.15, 4.45, -1.78, and .171 for cracking and -21.27, .0325, .972, -.00028, and .00022 for rutting. Determine the probability of pavement failure within $$\displaystyle{t}={5}$$ years and also $$\displaystyle{t}={10}$$ years.