1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexus [3.1K]
3 years ago
5

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

l-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a level of significance, does there appear to be a difference in the ability of the brands to absorb water?
Mathematics
1 answer:
arlik [135]3 years ago
3 0

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:

<em>The question is incomplete:</em>

<em>The significance level is 0.05.</em>

<em>The data is:</em>

<em>Brand X: 91, 100, 88, 89</em>

<em>Brand Y: 99, 96, 94, 99</em>

<em>Brand Z: 83, 88, 89, 76</em>

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.

You might be interested in
MJ solved the equation -5x - 16 = 5
Andrei [34K]

Answer:

Step-by-step explanation: He add 16 together you are not suppose to add 16 you are suppose to add 5 together so instead of 16 + 16 you do 16+ 5

3 0
3 years ago
Two consecutive even whole numbers have a product of 360. What is the smaller of the<br> two number?
Fed [463]

Answer:

let one even number be N

and another even number be N(N+2)

N(N+2)=360

n^2+2n-360=0

n^2+20n-18n-360=0

value of N= -20 ,18

but -20 not accepted

smaller number 18

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
PLEASE ANSWER ILL GIVE 5 STARS AND A HEART!!!
r-ruslan [8.4K]

Answer:

120

Step-by-step explanation:

5x6 = 30

30x4= 120

7 0
2 years ago
Terri is rewriting 7^13 in expanded form. How many factors should she use in her expression?
Mazyrski [523]
She should use 13 factors.
All 13 factors are the same thing . . . 7 .

7^13 should be written as 7¹³ .

It means:  7·7·7 · 7·7·7 · 7·7·7 · 7·7·7 · 7
6 0
3 years ago
Read 2 more answers
It took Sharon 4 hours to drive to her grandmother's house. Her grandmother lives 140 miles from Sharon.
Vladimir [108]

Answer:

You're right its B or 35

Step-by-step explanation:

Just divide 140 by 4 u get 35

3 0
3 years ago
Read 2 more answers
Other questions:
  • Rita has a loan of $45,580. This loan has a simple interest rate of 4% per year. What is the amount of interest that Rita will b
    9·2 answers
  • Point C is graphed on a number line at –7. Point D is 13 units away from point C on the number line.
    9·1 answer
  • A customer buys 3 bottles of water for ninety-nine cents each seven percent tax on each bottle what is the total bill
    5·2 answers
  • How do I round 47,283 to the nearest 100,000
    6·1 answer
  • Find either of the values of x<br> 2x^2+3x-2=3
    7·1 answer
  • Total profit P is defined as total revenue R -= total cost​ C, and is given by the function Upper P left parenthesis x right par
    13·1 answer
  • 331 students was on a field trip. Six buses were filled and 7 students traveled in cars. How many were in each bus?​
    6·1 answer
  • Which two recipes have equivalent ratios of cups of flour needed to the number of cookies?
    11·1 answer
  • Can someone help me please I am losing my mind
    6·1 answer
  • A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!