A box of dried fruit has 51 calories in 3 servings. how many calories are in 1 serving?

(a) For the accompanying data set, draw a scatter diagram of the data.

lidiya [134]

Answer:

a) n=5 $\sum x = 30, \sum y = 25, \sum xy = 162, \sum x^2 =206, \sum y^2 =155$

$r=\frac{5(162)-(30)(25)}{\sqrt{[5(206) -(30)^2][5(155) -(25)^2]}}=0.42967$

So then the correlation coefficient would be r =0.430 rounded

b) Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

Because the correlation coeffcient is positive and the absolute value of the correlation coefficient 0.430 is not greater than the critical value for this dataset, no linear relation exists between x and y.

And the reason is because we fail to reject the null hypothesis.

Step-by-step explanation:

Part a

We have the following data:

x: 2 6 6 7 9

y: 3 2 6 9 5

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=5 $\sum x = 30, \sum y = 25, \sum xy = 162, \sum x^2 =206, \sum y^2 =155$

$r=\frac{5(162)-(30)(25)}{\sqrt{[5(206) -(30)^2][5(155) -(25)^2]}}=0.42967$

So then the correlation coefficient would be r =0.430 rounded

Part b

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degreed of freedom. df=n-2=5-2=3

In our case the value for the statistic would be:

$t=\frac{0.430\sqrt{5-2}}{\sqrt{1-(0.430)^2}}=0.825$

The critical value for n =5 is given by the table attached. We can see that the critical value is $r_{crit}= 0.878$ , and then the final conclusion would be:

Because the correlation coeffcient is positive and the absolute value of the correlation coefficient 0.430 is not greater than the critical value for this dataset, no linear relation exists between x and y

And the reason is because we fail to reject the null hypothesis.

4 0

2 years ago

Find the sum 93.5+8.7

SIZIF [17.4K]

Answer:

102.2 is your answer

hope this helped you

please mark as the brainliest (ㆁωㆁ)

4 0

2 years ago

Read 2 more answers

Got a question g+ 3 over 6 = 15 what equals g?

Eva8 [605]

Answer:

g=18

Step-by-step explanation:

4 0

2 years ago

Help me with 2 of these. If u answer both put question 1 — and question 2 —

matrenka [14]

Answer:1 is b and 2 is d

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers

An investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were be

lisov135 [29]

Answer:

cohort study

Step-by-step explanation:

Given that an investigator reviewed the medical records of 200 children seen for care at Boston Medical Center in the past year who were between the ages 8 and 12 and identified 40 children with asthma. He also identified 40 children of the same ages who were free of asthma. Each child and their family were interviewed to assess whether there might be an association between certain environmental factors such as exposure to second-hand smoke.

The objective of this experiment is to test the causes of the disease asthma and to find the risk factors and environment causing this disease.

So this cannot come under randomized control nor case control.

Cross over study is to put to two different environments two groups and study. But here nothing is influenced actual environments are studied

Hence this comes under cohort study

3 0

2 years ago