11x-6=60 please give details

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$

Now we calculate the F statistic as:

$F=MSB/MSE=172/23.78=7.23$

The degrees of freedom of the numerator are:

$dfn=a-1=3-1=2$

The degrees of freedom of the denominator are:

$dfd=N-a=3*4-3=12-3=9$

The P-value of F=7.23, dfn=2 and dfd=9 is:

$P-value=P(F>7.23)=0.01342$

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

3 0

3 years ago

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected fro

Ksju [112]

Answer:

d. 0.133

Step-by-step explanation:

-Standard error is calculated using the formula:

$E=\frac{\sigma}{\sqrt{n}}\\\\\sigma-=standard \ deviation\\n=sample \ size$

#We substitute the given values in the formula to solve for E:

$E=\frac{\sigma}{\sqrt{n}}\\\\=\frac{1.2}{\sqrt{81}}\\\\=0.133$

Hence, the standard error is 0.133 and the correct option is d

7 0

3 years ago

Can someone please help me with this question about given two points?Please help ASAP!!! :(

KonstantinChe [14]

Answer:

The order of subtraction is not important in any of the coordinates

Step-by-step explanation:

Distance Between Two Points

Given two points (x1,y2) (x2,y2), the distance between them is given by the formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The difference between both coordinates is squared, then added, and finally extracted the square root.

Based on the principle that

$a*a=a^2$

and also

$(-a)(-a)=a^2$

We can notice it doesn't matter the sign of a the square of a is always positive. If we had subtracted in the opposite way, the distance would have resulted in exactly the same. In other words, the above formula is exactly the same as

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$