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3 years ago

A surplus is

Mathematics

2 answers:

pantera1 [17]3 years ago

8 0

It is when you spend less money than you have in income because a surplus is when there is extra money left over.

Rashid [163]3 years ago

7 0

I believe its when you spend less because surplus is what you have excess so if you spend less than you have more money left over

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

anyanavicka [17]

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!

4 0

2 years ago

F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the

nadezda [96]

The correct answer is actually the last one.

The second derivative $f''(x)$ gives us information about the concavity of a function: if $f''(x)$ then the function is concave downwards in that point, whereas if $f''(x)>0$ then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, $f''(8)=5$

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that $f(x)$ passes through the origin, so $f(0)=0$ . Now translate the function upwards, for example. we have that $f(x)+k$ doesn't pass through the origin, but the second derivative is always $f''(x)$ . So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative $f'(x)$ . In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0

2 years ago

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.3degrees°F and a standard deviation of 0.6

mylen [45]

<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n=106

Sample mean : $\overline{x}=98.3^{\circ}\ F$

Standard deviation : $\sigma= 0.69^{\circ}F$

Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Then , 99% confidence interval estimate of the mean body temperature of all healthy humans will be :-

$98.3\pm (2.576)\dfrac{0.69}{\sqrt{106}}\\\\\approx98.3\pm0.173=(98.3-0.173,\ 98.3+0.173)=(98.127,\ 98.473)$

Since 98.6 is higher than the upper limit of the confidence interval (98.473), then this suggest that the mean body temperature could be lower then 98.6 degrees.

The best estimate of population mean is always the sample mean. $\mu=\overline{x}=98.3^{\circ}\ F$