1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ket [755]
3 years ago
10

Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality ra

tes 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)
230 15.8
264 15.6
359 15.5
482 15.3
531 14.9

1. What are the null and alternative​ hypotheses?
2. Construct a scatterplot.
3. The linear correlation coefficient r is
4. The test statistic t is
5. 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.

Mathematics
1 answer:
anyanavicka [17]3 years ago
4 0

Answer:

Because the​ P-value is _(<u>0.02)  less </u> than the significance level 0.05​, there <u> is </u> 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.

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

Step-by-step explanation:

Hello!

The study variables are:

X₁: Weight of imported lemons.

X₂: Car crash fatality rate.

The objective is to test if the imported lemons affect the occurrence of car fatalities. To do so you are asked to use a linear correlation test.

I've made a Scatterplot with the given data, it is attached to the answer.

To be able to use the parametric linear correlation you can use the parametric test (Person) or the nonparametric test Spearman. For Person, you need your variables to have a bivariate normal distribution. Since one of the variables is a discrete variable (ratio of car crashes) and the sample is way too small to make an approximation to a normal distribution, the best test to use is Spearman's rank correlation.

This correlation coefficient (rs) takes values from -1 to 1

If rs = -1 this means that there is a negative correlation between the variables

If rs= 1 this means there is a positive correlation between the variables

If rs =0 then there is no correlation between the variables.

The hypothesis is:

H₀: There is no linear association between X₁ and X₂

H₁: There is a linear association between X₁ and X₂

α: 0.05

To calculate the Spearman's correlation coefficient you have to assign ranks to the observed values of each variable, from the smallest to the highest). Then you have to calculate the difference (d)between the ranks and the square of that difference (d²). (see attachment)

The formula for the correlation coefficient is:

rs= 1 - \frac{6* (sum of d^2)}{(n-1)n(n+1)}

rs= 1 - \frac{6* (40)}{4*5*6}

rs= -1

For this value of the correlation coefficient, the p-value is 0.02

Since the p-value (0.02) is less than the significance level (0.05) the decision is to reject the null hypothesis. In other words, there is a linear correlation between the imported lemons and the car crash fatality ration, this means that the modification in the lemon import will affect the car crash fatality ratio.

Note: the correlation coefficient is negative, so you could say that there is a correlation between the variables and this is negative (meaning that when the lemon import increases, the car crash fatality ratio decreases)

I hope it helps!

You might be interested in
Find the midpoint of the segment with the given endpoints (5,-9) and (-2,-2)
QveST [7]
Another way to solve this is to use the Midpoint Formula.  The midpoint of a segment joining points (x_1,y_1) and (x_2,y_2) is

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right)

So the midpoint of your segment is

\left(\frac{5+(-2)}{2},\frac{-9+(-2)}{2}\right) = \left(\frac{3}{2},-\frac{11}{2} \right)

Perhaps it helps to see that the x-coordinate of the midpoint is just the average of the x-coordinates of the points.  Ditto for the y-coordinate of the midpoint; just average the y's.
6 0
3 years ago
1001112 = [ ? ]10<br> ?<br> what number belongs where the question mark is
EleoNora [17]

I suppose you're supposed to convert 100111 from base 2 to base 10. We have

100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}

so the missing number is 39.

4 0
3 years ago
84 2/3% to a fraction in lowest terms
RoseWind [281]

The evaluation of 84 2/3% to a fraction in its lowest term is \mathbf{ \dfrac{127}{150} }

<h3>What is a fraction?</h3>

Fractions are sections or parts of a whole. They are divided into two parts, the numerator, and the denominator.

From the given information, we are to convert a mixed fraction into its lowest terms. By doing that, we are to convert it to an improper fraction.

\mathbf{= 84 \dfrac{2}{3}\%}

\mathbf{= \dfrac{(84 \times 3)+2}{3} \%}

\mathbf{= \dfrac{254}{3} \%}

\mathbf{= \dfrac{254}{3} \times \dfrac{1}{100}}

\mathbf{= \dfrac{254}{300} }

Divide both the numerator and denominator by (2)

\mathbf{= \dfrac{127}{150} }

Learn more about fractions here:

brainly.com/question/78672

#SPJ1

3 0
1 year ago
What are the solutions to the equation 13x? - 17x + 7 = 0?<br> ©
ICE Princess25 [194]

Answer:

x=7/4

Step-by-step explanation:

13x-17x+7=0

-4x+7=0

-4x+7-7=0-7

-4x=-7

-4x/-4=-7/-4

x=7/4

8 0
3 years ago
Can someone help me solve this
Phantasy [73]
The picture is white I can’t help you sorry
6 0
2 years ago
Other questions:
  • For her phone service, Lucy pays a monthly fee of $18, and she pays an additional $0.05 per minute of use. The least she has bee
    8·1 answer
  • Is 7/11 a rational number
    15·2 answers
  • What is the value of 6n-2
    14·1 answer
  • Find the distance between points P and Q
    8·1 answer
  • Where is the answer to the expression 3 - 6 located on a horizontal number line? O 3 units to the left of 3 O 3 units to the rig
    11·1 answer
  • The yearbook club had a meeting. The meeting had 30 people, which is three-fifths of the club. How many people are in the club?
    11·1 answer
  • An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at th
    5·1 answer
  • Fill in the blanks :)
    6·1 answer
  • WILL MARK BRAINLIEST PLS HELP ITS DUE
    7·2 answers
  • Sorry forgot to post pictures of the question on last post (here there are)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!