Mathematics, 03.12.2019 12:31 spowell5993

You are interested in knowing whether wealthier people are happier. you collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. upon analyzing the results, you find that the correlation coefficient has a value of −0.25. on the basis of this data, respond to the following:
how would you interpret the correlation coefficient in terms of strength and direction?
how would the results be affected if you increased the number of subjects in the study to one thousand? why might that affect the overall correlation?
how important is it to randomly select subjects? explain in detail using an example of a sample that might not be truly representative of the population.

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Answer from: oof4457

Well if it is a negative value then it has a negative correlation. Meaning that as one goes up then the other goes down. It could mean that if money was x, and happiness was y then the more money you make then the less happiness you have. But also since it was a value of .25 that means it is a weak correlation so there is not much value to this.

With any data collection you have the more participates the more accurate the data. Since you only initially took 50, then by taking 950 more the data could be completely flipped and could have a positive strong correlation. Although there is no way to tell what the results might be.

Randomly selected would be very important. A sample set that wouldnt be a true representation of the population would be professional athletes. Generally speaking they are very very wealthy and for the more part they are generally happy because they are doing what they love more than anything. I would assume that not everyone that is wealthy like that has the same passion for their work and the same happiness in life. They are just playing a game that they love and getting millions for it. Definitely doesn't represent the population.

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

Answer from: Quest

Answers4.) -1/205.) -1/406.) -55/127.) -3/4
Answer these i don’t know at all and need fast

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