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Sav [38]
3 years ago
8

A set of n = 5 pairs of x and y values has ssx = 10, ssy = 40 and sp = 10. for these data, the pearson correlation is

Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
5 0

r = correlation coefficient

r = \frac{Sxy}{\sqrt{Sxx * Syy}}

If: Sxx = 10, Syy = 40, Sxy = 10, then:

r = \frac{10}{\sqrt{10 * 40}} \\\\ = \frac{10}{\sqrt{400}}  \\\\ = \frac{10}{20} \\\\ = \frac{1}{2}

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Look at the right-angled triangle ABC.
olga_2 [115]

Answer:

∠x = 90°

∠y = 58°

∠z = 32°

Step-by-step explanation:

he dimensions of the angles given are;

∠B = 32°

Whereby ΔABC is a right-angled triangle, and the square fits at angle A, we have;

∠A = 90°

∠B + ∠C = 90° which gives

32° + ∠C = 90°

∠C = 58°

∠x + Interior angle of the square = 180° (Sum of angles on a straight line)

∠x + 90° = 180°

∠x = 90°

∠x + ∠y + 32° = 180° (Sum of angles in a triangle)

90° + ∠y + 32° = 180°

∠y = 180 - 90° - 32° = 58°

∠y + ∠z + Interior angle of the square = 180° (Sum of angles on a straight line)

58° + ∠z +90° = 180°

∴ ∠z = 32°

∠x = 90°

∠y = 58°

∠z = 32°

8 0
2 years ago
What is AB? in the right triangle shown, AC = BC = 2
saul85 [17]

Answer:

2.83

Step-by-step explanation:

using the pythagorean theorem, AB=\sqrt{AC^2+BC^2}=\sqrt{2^2+2^2}≈2.83

6 0
3 years ago
Read 2 more answers
Give one example of when you would use the friendly numbers strategy to subtract. Explain why.
ziro4ka [17]

In the <span>addition process</span> this usually involves:

<span><span>rounding numbers up to the nearest multiple of 10 or 100 </span>subtracting the extras that were added at the end.</span>

In the subtraction process this usually involves subtracting too much and completing the calculation by putting some back.


6 0
3 years ago
Read 2 more answers
To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of t
nikklg [1K]

Answer:

t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805  

p_v =P(t_{(18)}

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance

Step-by-step explanation:

Data given and notation

We can calculate the sample mean and deviation with these formulas:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_{1}=19.1 represent the mean for the sample mean for 1

\bar X_{2}=23.3 represent the mean for the sample mean for 2

s_{1}=4.818 represent the sample standard deviation for the sample 1

s_{2}=5.559 represent the sample standard deviation for the sample 2

n_{1}=10 sample size selected 1

n_{2}=10 sample size selected 2

\alpha represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the average time taken when training under method 1 is less than the average time for Method 2, the system of hypothesis would be:

Null hypothesis:\mu_{1} \geq \mu_{2}

Alternative hypothesis:\mu_{1} < \mu_{2}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805  

P-value

The first step is calculate the degrees of freedom, on this case:

df=n_{1}+n_{2}-2=10+10-2=18

Since is a one sided test the p value would be:

p_v =P(t_{(18)}

Conclusion

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance

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2 years ago
What are the factors of 37, 51, and 45? i just dont get it
lbvjy [14]
37 is prime, so it's only factors are 1 and 37 
<span>51 has factors of 1,51 and 3,17 </span>
<span>45 has factors of 1,45 ; 3,15 and 5,9 </span>
5 0
3 years ago
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