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1:


style="background-color:transparent;color:rgb(0,0,0);">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

229

266

359

480

532

Crash Fatality Rate

15.8

15.7

15.4

15.3

14.9


What are the null and alternative​ hypotheses?

A. H0​: p=0

H1​:p≠0


B. H0​:ρ=0

H1​:ρ>0


C. H0​:ρ=0

H1​:ρ<0


D. H0​: p≠0

H1​:ρ=0


Construct a scatterplot. Choose the correct graph below.

A. A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 14.9); (270, 15.3); (360, 15.4); (480, 15.7); (530, 15.8). All horizontal coordinates are approximate.


B.A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.8); (270, 15.7); (360, 15.4); (480, 15.7); (530, 15.8). All horizontal coordinates are approximate.


C. A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.8); (270, 15.7); (360, 15.4); (480, 15.3); (530, 14.9). All horizontal coordinates are approximate.


D. A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (200, 14.9); (230, 15.8); (330, 16.2); (400, 15.1); (560, 15.3). All horizontal coordinates are approximate.

The linear correlation coefficient r is

nothing



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 in an increase in car fatality rates.

B. The results suggest that imported lemons cause car fatalities.

C. The results suggest that an increase in imported lemons causes car fatality rates to remain the same.

D. The results do not suggest any​ cause-effect relationship between the two variables.









2:

a. Using the pairs of values for all 10 ​points, find the equation of the regression line.

b. After removing the point with coordinates (1,2)​, use the pairs of values for the remaining 9 points and find the equation of the regression line.

c. Compare the results from parts​ (a) and​ (b).



0

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4

6

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10

x

A scatterplot has a horizontal x-scale from 0 to 10 in increments of 1 and vertical y-scale from 0 to 10 in increments of 1. Ten points are plotted with nine points, (3, 5), (4, 5), (5, 5), (3, 6), (4, 6), (4, 6), (5, 6), (3, 7), (4, 7), and (5, 7), forming a square and the tenth point (1, 2) being below and to the left of the square.

a. What is the equation of the regression line for all 10 ​points?

y =__+__x​ 


b. What is the equation of the regression line for the set of 9 ​points? y = ____


c. Choose the correct description of the results below.


A. The regression line is very similar in both cases.

B. The removal of the point has a significant impact on the regression line.

C. The regression line​ changes, but the change is small.

D. There is no regression line for the second case because the data are in a pattern.




3:

The claim is that the proportion of peas with yellow pods is equal to 0.25​ (or 25%). The sample statistics from one experiment include 570 peas with 146 of them having yellow pods. Find the value of the test statistic.

The value of the test statistic is

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