Sheila needs 3 3 4 cups our to make cookies. Which fraction is equivalent to 3 3 4 cups of our?

Which statements about residuals are true for the least-squares regression line? I. A random scattering of residuals indicates t

Daniel [21]

Answer:

II. The sum of the residuals is always 0.

Step-by-step explanation:

A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.

For any least-squares regression line, the sum of the residuals is always zero.

Basically, residuals are used to measure or determine whether or not the line of regression is a good fit or match for the data by subtracting the difference between them i.e the predicted y value and the actual y value, for the x value respectively.

Hence, the statement about residuals which is true for the least-squares regression line is that the sum of the residuals is always zero (0).

7 0

3 years ago

Carmen works at a pet store.To feed 8 cats, she empties four 6-ounce cans of cat food into a large bowl.Carmen divides the food

balu736 [363]

Answer:

0.75 oz

Step-by-step explanation:

8 cats divided by 6-oz cans=0.75 oz each

7 0

3 years ago

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

Jose wants to rewrite 24+9 using the greatest common factor and the distributive property. Which expression should he write?

Reil [10]

First get the factors of 24: 2*2*2*3Then the factors of 9: 3*3 Comparing the factors, the GCF is 3 Then you can rewrite the expression: 3*8 + 3*3 At this point, I'm not sure whether what you mean is really distributive property or not since this case is more of a factoring. 3*(8+3)

4 0

3 years ago

The length of s is 2/3 the length of t. If s has an area of 368 cm squared find the perimeter of the figure

ser-zykov [4K]

$s = \frac{2}{3}t
\\\ \frac{2}{3}t*t = \frac{2}{3}t^2
\\\ \frac{2}{3}t^2 = 368
\\\ t^2 = \frac {3}{2}368
\\\ t^2 = 552
\\\ t \approx 23.5
\\\ s \approx 15.6
\\\ P \approx 78.2$

3 0

3 years ago

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