Answer:
The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4
Step-by-step explanation:
Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.
The equation can also be written as (76a³+19a²)+(16a+4) = 0
On factorizing out the common terms from each parenthesis, we will have;
19a²(4a+1)+4(4a+1) = 0
(19a²+4)(4a+1) = 0
19a²+4 = 0 and 4a+1 = 0
From the first equation;
19a²+4 = 0
19a² = -4
a² = -4/19
a = ±√-4/19
a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)
From the second equation 4a+1 = 0
4a = -1
a₃ = -1/4
A statistics pratitioner took a random sample of 30 observations from a population whose standard deviation is 15 and computed the sample mean to be 50. The 90% confidence inverval for the mean will be ____________ and ______________.
Answer:
[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]
[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]
The 90% confidence inverval for the mean will be 45.509 and 54.491
Step-by-step explanation:
Information given
[tex]\bar X= 50[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma= 15[/tex] represent the sample standard deviation
n= 30 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]50-1.64\frac{15}{\sqrt{30}}=45.509[/tex]
[tex]50+1.64\frac{15}{\sqrt{30}}=54.491[/tex]
The 90% confidence inverval for the mean will be 45.509 and 54.491
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. Find the rate of growth after 3 hours.
Step-by-step explanation:
Rate of growth equals 420/100 = 4.2 times per hour
So after t=three hours,
size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,
round to nearest unit 7409 bacteria after three hours (after initial size of 100).
Answer:
a) 100•4.2^t
b) P(3)= about 7409 bacteria
c) P’(3)= about 10,632 bacteria per hour
d) t= about 3.2 hours
Step-by-step explanation:
Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. At one school, the average amount of time that spend watching television each week is The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of
Answer:
Left tailed test
Step-by-step explanation:
A two tailed test usually determined by the alternative hypothesis involves both the less than and the greater than option.
A left tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the less than option.
A right tailed test corresponds to an alternative hypothesis having just one of either options (less than and the greater than option) usually the greatest than option.
In this experiment, the null hypothesis is the average amount of time that spend watching television each week is ---
He introduces a campaign to encourage the students to watch less television and then performs a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. The alternative hypothesis would be: u < ---. This means that this test is a left tailed test.
what is the product?
(x-3)(2x²-5x+1)
C) 2x³-11x²+16x-3
Answer:
2x^3-11x^2+16x-3
Step-by-step explanation:
1) multiply each term inside the parentheses with all other terms:
(x*2x^2)=2x^3
x*-5x=-5x^2
x*1=x
-3*2x^2=-6x^2
-3*-5x=15x
and
-3*1=-3
so
2x^3-5x^2+x-6x^2+15x-3
is our equation
to simplify:
2x^3-11x^2+16x-3 is the answer
Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person. The Census Bureau would like to set α = 0.05. Use the critical value approach to test this hypothesis. Explain.
Answer:
For this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:
[tex] z_{\alpha}= 1.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27
Step-by-step explanation:
We have the following dataset given:
[tex] X= 43[/tex] represent the households consisted of one person
[tex]n= 125[/tex] represent the sample size
[tex] \hat p= \frac{43}{125}= 0.344[/tex] estimated proportion of households consisted of one person
We want to test the following hypothesis:
Null hypothesis: [tex]p \leq 0.27[/tex]
Alternative hypothesis: [tex]p>0.27[/tex]
And for this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:
[tex] z_{\alpha}= 1.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27
An item is regularly priced at $83. It is on sale for 95% off the regular price.
Answer:
Step-by-step explanation:
Regular price = $ 83
Discount = 95% of 83
= 0.95 * 83
= $ 78.85
Price after discount = 83 - 78.85
= $ 4.15
Answer:
$4.15
Step-by-step explanation:
Multiply 83 by .05 to get the new price of $4.15. Additionally, multiply 83 by .95 to get the amount taken off ($78.85).
asdasd I don't actually have a question I accidentally typed this
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Answer:
that's cool . . .
\is ok everyone makes mistakes
Anyone can help me with my math homework please?
Answer:
Step-by-step explanation:
hello,
so we know y in terms of t and x in terms of t and we need to find y in terms of x
[tex]x=21t^2<=>\sqrt{x}=\sqrt{21}*t \ \ as \ \ t>=0 \ \ So\\t=\sqrt{\dfrac{x}{21}}[/tex]
and then
[tex]y=f(x)=3\sqrt{\dfrac{x}{21}}+5=\sqrt{\dfrac{9x}{21}}+5=\sqrt{\dfrac{3x}{7}}+5[/tex]
hope this helps
Factor the polynomial expression x4 – 6x2 + 5.
Answer:
Hello!
______________________
x4 – 6x2 + 5
= ( x^2 - 5) ( x + 1 ) ( x - 1 )
Step-by-step explanation: Factor.
Hope this helped you!
When 440 junior college students were surveyed, 200 said they have a passport. Construct a 95% confidence interval for the proportion of junior college students that have a passport.
The Confidence Interval is 0.403 < p < 0.497
What is Confidence Interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given:
Sample proportion = 190/425
= 0.45
Now, [tex]\mu[/tex] = 1.96 x √[0.45 x 0.55/425]
[tex]\mu[/tex] = 0.047
So, 95% CI:
0.45-0.047 < p < 0.45+0.047
0.403 < p < 0.497
Learn more about Confidence Interval here:
https://brainly.com/question/24131141
#SPJ5
The probability distribution for a
random variable x is given in the table.
Answer: 79% probability
Step-by-step explanation:
.17 + .13 + .33 + .16 = .79
.79 x 100 = 79%
Answer:
.79
Step-by-step explanation:
Will give brainliest answer
Answer:
98 unitsSolution,
Circumference of circle = 615.44 units
Radius = ?
Now,
Circumference of circle = 615.44
[tex]2\pi \: r = 615.44[/tex]
[tex]2 \times 3.14 \times r = 615.44[/tex]
[tex]6.28r = 615.44[/tex]
[tex]r = \frac{615.44}{6.28} [/tex]
[tex]r = 98 \: units[/tex]
Hope this helps...
Good luck on your assignment...
Unit sales for new product ABC has varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 330 274 492 371 160 283 164 What is the (population) standard deviation of the data
Answer:
Approximately standard deviation= 108
Step-by-step explanation:
Let's calculate the mean of the data first.
Mean =( 330+ 274+ 492 +371 +160+ 283+ 164)/7
Mean= 2074/7
Mean= 296.3
Calculating the variance.
Variance = ((330-296.3)²+( 274-296.3)²+ (492-296.3)²+( 371-296.3)²+ (160-296.3)² (283-296.3)²+(164-296.3)²)/7
Variance= (1135.69+497.29+38298.49+5580.09+18577.69+176.89+17503.29)/7
Variance= 81769.43/7
Variance= 11681.347
Standard deviation= √variance
Standard deviation= √11681.347
Standard deviation= 108.080
Approximately 108
if karen was 27 and her oldest brother was 29 years older and and there dad was 22 when Karen was born how old is the dad?
Answer:
49
Step-by-step explanation:
When Karen was born, the dad is 22 so Karen is now 27 which means the dad is 22+27= 49
Answer:
Their father is 49.
Step-by-step explanation:
Her father had her when he was 22, meaning that he is 22 years older than Karen. Karen is 27 right now, so her fathers age is (27+22) 49 years old.
Hope this helps!
solve for x enter the solution from least to greatest x^2+3x-28=0
Answer:
x+4=0,x=−4x−7=0,x=7
You can model that you expect a 1.25% raise each year that you work for a certain company. If you currently make $40,000, how many years should go by until you are making $120,000? (Round to the closest year.)
Answer:
94 years
Step-by-step explanation:
We can approach the solution using the compound interest equation
[tex]A= P(1+r)^t[/tex]
Given data
P= $40,000
A= $120,000
r= 1.25%= 1.25/100= 0.0125
substituting and solving for t we have
[tex]120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t[/tex]
dividing both sides by 40,000 we have
[tex](1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47[/tex]
dividing both sides by 0.005 we have
[tex]t= 0.47/0.005\\t= 94[/tex]
What is the equation of a line passes thru the point (4, 2) and is perpendicular to the line whose equation is y = ×/3 - 1 ??
Answer:
Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.
y= -3x+b
Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14
Finally, put in everything we've found to finish the equation.
y= -3x+14
Answer:
y = -3x + 14
Step-by-step explanation:
First find the reciprocal slope since it is perpendicular. Slope of the other line is 1/3 so the slope for our new equation is -3.
Plug information into point-slope equation
(y - y1) = m (x-x1)
y - 2 = -3 (x-4)
Simplify if needed
y - 2 = -3x + 12
y = -3x + 14
Identify the axis of symmetry and vertex of f(x) = –x2 –2x–1.
Answer:
Vertex: (-1, 0)
Axis of Symmetry: x = -1
Step-by-step explanation:
Use a graphing calc.
Susan decides to take a job as a transcriptionist so that she can work part time from home. To get started, she has to buy a computer, headphones, and some special software. The equipment and software together cost her $1000. The company pays her $0.004 per word, and Susan can type 90 words per minute. How many hours must Susan work to break even, that is, to make enough to cover her $1000 start-up cost? If Susan works 4 hours a day, 3days a week, how much will she earn in a month.
Answer:
46.3 hours of work to break even.
$1036.8 per month (4 weeks)
Step-by-step explanation:
First let's find how much Susan earns per hour.
She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:
0.004 * 90 = $0.36
Then, per hour, she will earn:
0.36 * 60 = $21.6
Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:
1000 / 21.6 = 46.3 hours.
She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.
If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:
48 * 21.6 = $1036.8
Answer:
46.3 hours of work to break even.
$1036.8 per month (4 weeks)
Step-by-step explanation:
What is the simplified form of this expression?
(-3x^2+ 2x - 4) + (4x^2 + 5x+9)
OPTIONS
7x^2 + 7x + 5
x^2 + 7x + 13
x^2 + 11x + 1
x^² + 7x+5
Answer:
Option 4
Step-by-step explanation:
=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]
Combining like terms
=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]
=> [tex]x^2+7x+5[/tex]
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9,8 and 7(separate number sum for each multiple). What is the sum of these three numbers?
Answer:
Sum of 2 digit = 48
Sum of 3 digit = 317
Sum of 4 digit = 3009
Total = 3374
Step-by-step explanation:
Given:
9, 8 and 7
Required
Sum of Multiples
The first step is to list out the multiples of each number
9:- 9,18,....,99,108,117,................,999
,1008
,1017....
8:- 8,16........,96,104,...............,992,1000,1008....
7:- 7,14,........,98,105,.............,994,1001,1008.....
Calculating the sum of smallest 2 digit multiple of 9, 8 and 7
The smallest positive 2 digit multiple of:
- 9 is 18
- 8 is 16
- 7 is 14
Sum = 18 + 16 + 14
Sum = 48
Calculating the sum of smallest 3 digit multiple of 9, 8 and 7
The smallest positive 3 digit multiple of:
- 9 is 108
- 8 is 104
- 7 is 105
Sum = 108 + 104 + 105
Sum = 317
Calculating the sum of smallest 4 digit multiple of 9, 8 and 7
The smallest positive 4 digit multiple of:
- 9 is 1008
- 8 is 1000
- 7 is 1001
Sum = 1008 + 1000 + 1001
Sum = 3009
Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit
Sum of All = 48 + 317 + 3009
Sum of All = 3374
consider the difference of squares identity a^2-2b^2=(a+b)(a-b)
Answer: a= 3x and b= 7
Step-by-step explanation:
^^
Find the total surface area of this triangular prism 13cm 5cm 12cm 9cm 15cm 20cm
Answer:
924 cm²
Step-by-step explanation:
The surface area is equal to the area of the two triangles + area of the three rectangles.
Area of two triangles:
12 × (9+5) × 1/2
= 84
84(2) = 168
Area of the three rectangles:
15 × 20 + 13 × 20 + 14 × 20
= 840
840 + 84
The surface area of the triangular prism is 924 cm².
(a +2b)2 + 4b² - a²
Answer:
a^2+4b^2+2a+4b
Step-by-step explanation:
(a +2b)2 + 4b² - a²
=2a+4b+4b^2+a^2
=a^2+4b^2+2a+4b
A survey of 400 non-fatal accidents showed that 189 involved the use of a cell phone. Determine a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone.
Answer:
[tex] X= 189[/tex] represent the number of non-fatal accidents involved the use of a cell phone
[tex] n=400[/tex] represent the sample size
And we want to find a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone and we can use the following formula:
[tex]\hat p=\frac{X}{n}[/tex]
And replacing we got:
[tex] \hat p=\frac{189}{400}=0.4725[/tex]
Step-by-step explanation:
For this problem we have the following info given:
[tex] X= 189[/tex] represent the number of non-fatal accidents involved the use of a cell phone
[tex] n=400[/tex] represent the sample size
And we want to find a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone and we can use the following formula:
[tex]\hat p=\frac{X}{n}[/tex]
And replacing we got:
[tex] \hat p=\frac{189}{400}=0.4725[/tex]
Prove that If A1, A2, ... , An and B1, B2,...,Bn are sets such that Aj ⊆ Bj for j = 1, 2, 3, ... , n, then ∪j=1nAj ⊆ ∪j=1nBj .
Answer:
This is proved using Proof by induction method. There are two steps in this method
Let P(n) represent the given statement ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
1. Basis Step: This step proves the given statement for n = 1
2. Induction step: The step proves that if the given statement holds for any given case n = k then it should also be true for n = k + 1.
If the above two steps are true this means that given statement P(n) holds true for all positive n and the mathematical induction P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true.
Step-by-step explanation:
Basis Step:
For n = 1
∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] = ∪[tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
We show that
∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = A₁ ⊆ B₁ = ∪[tex]{ {{1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] for n = 1
Hence P(1) is true
Induction Step:
Let P(k) be true which means that we assume that:
for all k with k≥1, P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true
This is our induction hypothesis and we have to prove that P(k + 1) is also true
This means if ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] holds for n = k then this should also hold for n = k + 1.
In simple words if P(k): ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true then ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is also true
∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex]
⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] As ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] As [tex]A_{k+1}[/tex] ⊆ [tex]B_{k+1}[/tex]
= ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
The whole step:
∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] = ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]A_{k+1}[/tex] ⊆ ∪[tex]{ {{k} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] ∪ [tex]B_{k+1}[/tex] = ∪[tex]{ {{k+1} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
shows that the P(k+1) also holds for ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex]
hence P(k+1) is true
So proof by induction method proves that P(n) is true. This means
P(n): ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]A_{j}[/tex] ⊆ ∪ [tex]{ {{n} \atop {j=1}} \right.[/tex] [tex]B_{j}[/tex] is true
Evelyn wants to estimate the percentage of people who own a tablet computer she surveys 150 indvidals and finds that 120 own a tablet computer. Identify the values needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.
0.10 0.05 0.025 0.01 0.005
1.282 1.645 1.960 2.326 2 576
Answer:
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Step-by-step explanation:
Confidence interval for the proportion of people who own a tablet:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{120}{150} = 0.8[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.576[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841[/tex]
Percentage:
Multiply the proportion by 100.
0.7159*100 = 71.59%
0.8841*100 = 88.41%
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level.
n Mean Std. Dev.
Midsize 31 25.8 2.56
SUV’s 31 22.68 3.67
Pickups 14 21.29 2.76
Answer:
Step-by-step explanation:
Hello!
You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.
n | Mean | Std. Dev.
Midsize | 31 | 25.8 | 2.56
SUV’s | 31 | 22.68 | 3.67
Pickups | 14 | 21.29 | 2.76
Be the study variables :
X₁: highway gas mileage of a midsize car
X₂: highway gas mileage of an SUV
X₃: highway gas mileage of a pickup truck.
Assuming these variables have a normal distribution and are independent.
The hypotheses are:
H₀: μ₁ = μ₂ = μ₃
H₁: At least one of the population means is different.
α: 0.01
The statistic for this test is:
[tex]F= \frac{MS_{Treatment}}{MS_{Error}}[/tex]~[tex]F_{k-1;n-k}[/tex]
Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.
For the treatments:
The degrees of freedom between treatments are k-1 (k represents the amount of treatments): [tex]Df_{Tr}= k - 1= 3 - 1 = 2[/tex]
The sum of squares is:
SSTr: ∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= grand mean, is the mean that results of all the groups together.
So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.
To calculate the grand mean you can sum the means of each group and dive it by the number of groups:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26
[tex]SS_{Tr}[/tex]= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689
[tex]MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33[/tex]
For the errors:
The degrees of freedom for the errors are: [tex]Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73[/tex]
The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:
[tex]MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52[/tex]
Now you can calculate the test statistic
[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56[/tex]
The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:
[tex]F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07[/tex]
If [tex]F_{H_0}[/tex] ≥ 4.07, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 4.07, do not reject the null hypothesis.
Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.
Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)
I hope this helps!
What is the value of x in equation 1/3 (12x -24) = 16
Thank you
Answer:
The value of x is x = 6
Step-by-step explanation:
[tex]\frac{1}{3}(12x - 24) = 16\\ 12x - 24 = 48\\12x = 48+ 24\\12x = 72\\12/12 = x\\72/12 = 6\\x=6[/tex]
Hope this helped! :)
Which of the following functions is graphed below
Answer:
the answer is C. y=[x-4]-2
Answer:
Step-by-step explanation:
Y=(x+4)-2