Answer:
1.56 hours
Step-by-step explanation:
300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.
Answer:
i thought the question said a 'HORSE' fills a hot tub...
Step-by-step explanation:
lol dont mind me i just want points :D
A local coffee house surveyed 317 customers regarding their preference of chocolate chip or cranberry walnut scones . 150 customers prefer the Cranberry Walnut Scones . 81 customers who responded were males and prefer the Chocolate Chip Scones . 172 female customers responded . Find the probability that a customer chosen at random will be a male or prefer the Chocolate Chip Scones .
1. 25.6%
2. 24.1%
3. 72.9%
4. 98.4%
Answer:
3. 72.9%
Step-by-step explanation:
Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.
So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:
P(M∪C) = P(M) + P(C) - P(M∩C)
Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:
P(M) = 145/317 = 0.4574
There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:
P(C) = 167/317 = 0.5268
Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate chip scones is:
P(M∩C) = 81/317 = 0.2555
Therefore, P(M∪C) is equal to:
P(M∪C) = 0.4574 + 0.5268 - 0.2555
P(M∪C) = 0.7287
P(M∪C) = 72.9%
Answer:
3. 72.9%
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.
There are 172 female customers and 317-172 = 145 male customers.
150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.
81 of those are male, so 167 - 81 = 86 are female.
So the total of desired outcomes is 86 + 145 = 231
Total outcomes:
317 total customers.
Probability:
231/317 = 0.729
So the correct answer is:
3. 72.9%
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
5*15 = 75Minimum value for the first four numbers would be:
1, 2, 3, 4Then the fifth number is:
75 - (1+2+3+4) = 75 - 10 = 65So the maximum difference is:
65 - 1 = 64Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matrix consistent? A. Yes, because the rightmost column of the augmented matrix is a pivot column. B. Yes, because the rightmost column of the augmented matrix is not a pivot column. C. No, because the rightmost column of the augmented matrix is a pivot column. D. No, because the rightmost column of the augmented matrix is not a pivot column.
Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
When Sunita weighed herself on Monday, she found that she had gained 1 1/4 kg. Earlier her weight was 46 3/8 kg. What was her weight on Monday? Please give me Statements! Please Do it fast(Its ok if you dont do it fast ok its not like that much of an urgent) #GoAwayCoronaVirus
Answer:
[tex]47\frac{5}{8}[/tex]
Step-by-step explanation:
Weight from before + Weight gained
[tex]46\frac{3}{8} +1\frac{1}{4}[/tex]
Convert to improper fractions.
[tex]371/8 + 5/4[/tex]
Find the common denominator.
[tex]371/8 + 10/8[/tex]
Add.
[tex]381/8[/tex]
Convert to a mixed fraction.
[tex]47\frac{5}{8}[/tex]
Answer:
47 5/8 kg
Step-by-step explanation:
Ealier weight + gained weight = Monday's weight
46 3/8 + 1 1/4
= 371/8 + 5/4
= 371/8 + 10/8
= 381/8
= 47 5/8 kg
The following data show the brand, price , and the overall score for stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from (lowest) to (highest). The estimated regression equation for these data is = 23.194 + 0.318x, where x = price ($) and y = overall score.
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
Required:
a. Compute SST, SSR, and SSE (to 3 decimals).
b. Compute the coefficient of determination r2.
c. What is the value of the sample correlation coefficient?
Answer:
a. SST = 1816
SSR = 1511.804
SSE = 465.804
b. Coefficient of determination, R² = 0.832491079
c. The correlation coefficient r = 0.8636
Step-by-step explanation:
y = 23.194 + 0.318·x
Where:
x = Price
y = Overall score
The observed data are given as follows;
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816
[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804
[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804
Coefficient of determination
[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832
Coefficient of correlation =
[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]
Ʃxy = 37500
Ʃx =600
Ʃy = 330
Ʃx² = 74950
Ʃy² = 19966
[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]
Which whole number can each term of the equation be multiplied by to eliminate the fractions before solving
Answer:
the least common denominator
Step-by-step explanation:
The least common denominator is that number. It is the least common multiple of the denominator values.
__
Simply multiplying by the product of the denominators will eliminate fractions, but may require reduction of fractions in the answer. If the "fractions" are rational expressions, extraneous solutions may be introduced.
Classify the following triangle check all that apply. 98,41,41
Answer:
B. Isosceles triangle
Answer: obtuse and isosceles <3
Step-by-step explanation:
Fraction - Subtrction : 15 5/11 - 7 3/12
Answer:
[tex]= 8 \frac{27}{132} = 8\frac{9}{44}\\ [/tex]
Step-by-step explanation:
[tex]15 \frac{5}{11} - 7 \frac{3}{12} \\ \frac{170}{11} - \frac{87}{12} \\ \frac{2040 - 957}{132} \\ = \frac{1083}{132} \\ = 8 \frac{27}{132} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
8 9/44.
Step-by-step explanation:
15 5/11 - 7 3/12
= 15 - 7 + 5/11 - 1/4 The LCD of 4 and 11 is 44 so we have:
15 - 7 + 20/44 - 11/44
= 8 + 9/44
= 8 9/44.
Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year and nearly 80% of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2009). The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is 2400. A sample of SAT scores for the combined three-part SAT are as follows:
1665 1275 1650 1590 1475 1490
1525 2135 1560 1880 1680 1560
1355 1280 1150 1420 14409 4016
4510 6014 8517 5512 6013 9017
8015 8519 901 3751 7301 1755
Required:
a. Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200.
b. Comment on the shape of the distribution.
c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?
Answer:
Step-by-step explanation:
Hello!
The sample shows the scores for the combined three-part SAT.
Raw data in first attachment.
a.
To arrange the data in a frequency table using class intervals you have to determine the number of intervals you want to use and calculate their width. In this case, the width is given and so is the lower limit of the first interval, you calculate the successive limits by adding the width. The lower limit of the next interval will be the upper limit of the previous one:
1) 800 + 200= 100
First interval [800; 1000)
2) 1000 + 200
Second interval
[1000; 1200)
And so on until you reach the maximum value of the data set,
[1200; 1400)
[1400; 1600)
[1600; 1800)
[1800; 2000)
[2000; 2200)
Then you have to order the data from least to greatest and count how many observations correspond to each value, this way you'll determine the observed frequency for each interval.
Table and histogram in second attachment.
b.
As you can see in the histogram, this distribution is symmetrical centered in the interval [1400; 1600) and there are no outliers observed.
c.
Values around 1400-1600 are the most common ones while scores around 800-1000 or 2000-2200 are more uncommon, in this sample it seems the probability to obtain a perfect score for the combined three-part SAT is extremely low.
I hope you have a nice day!
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):_________.
Before visit: 57.1 94.6 49.2 77.4 43.2After visit: 63.5 101.8 57.8 81.2 41.9Do the data indicate that the average net sales improved? (Use a= 0.05)
Answer:
Step-by-step explanation:
Corresponding net sales before 1 month and after 1 month form matched pairs.
The data for the test are the differences between the net sales before and after 1 month.
μd = the net sales before 1 month minus the net sales after 1 month.
Before after diff
57.1 63.5 - 6.4
94.6 101.8 - 7.2
49.2 57.8 - 8.6
77.4 81.2 - 3.8
43.2 41.9 1.3
Sample mean, xd
= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94
xd = - 4.94
Standard deviation = √(summation(x - mean)²/n
n = 5
Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872
Standard deviation = √(60.872/5
sd = 3.49
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4
2) The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 4.94 - 0)/(3.49/√5)
t = - 3.17
We would determine the probability value by using the t test calculator.
p = 0.017
Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.
Simplify the expression. Write the answer using scientific notation. (7 × 105)2 a. 4.9 × 1010 b. 4.9 × 1011 c. 4.9 × 109 d. 49 × 1010
Answer:
b. 4.9 × 1011
Step-by-step explanation:
Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2
We open the parenthesis. This may first be expressed as
7² × 10⁽⁵⁾²
Then expand,
= 49 × 10¹⁰
To put in scientific notation, 49 = 4.9 × 10
Hence the expression becomes
= 4.9 × 10 × 10¹⁰
Using the laws of indices
= 4.9 × 10¹¹ in scientific notation
Answer:
4.9 × 1011
Step-by-step explanation:
I did it in grandpoint
1. Mrs. Verner's class has
a total of 15 students. If 8
of them are girls, what
percentage are boys?
Answer:
46.7%
Step-by-step explanation:
Given:
Total number of students in Mrs. Verner's class = 15
Number of girls = 8
To find: percentage are boys
Solution:
Percentage of boys = ( Number of boys / Total number of students ) × 100
Number of boys = Total number of students - Number of girls = 15 - 8 = 7
So,
Percentage of boys = [tex]\frac{7}{15}[/tex] × 100 = 46.7%
Suppose that the raw daily oxygen purities delivered by an air-products supplier have a standard deviation LaTeX: \sigma\approx.1 σ ≈ .1 (percent), and it is plausible to think of daily purites as independent random variables. Approximate the probability that the sample mean LaTeX: \frac{ }{X} X of n = 25 delivered purities falls within .03 (percent) of the raw daily purity mean, LaTeX: \mu μ .
Answer:
There is a probability of 86.6% that the sample mean falls within 0.03 percent of the raw purity mean.
Step-by-step explanation:
We have a population standard deviation of σ ≈ 0.1.
We have a sample of size n=25.
Then, we have a sampling distribution, which has a standard deviation for the sample mean that is:
[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{25}}=\dfrac{0.1}{5}=0.02[/tex]
Now, we can calculate a z-score for a deviation of 0.03 percent from the mean as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{0.03}{0.02}=\dfrac{0.03}{0.02}=1.5[/tex]
Note: we considered that the margin is ±0.03.
Then, the probability is:
[tex]P(|X-\mu|<0.03\%)=P(|z|<1.5)=0.866[/tex]
Can someone help me with this I’m sorry I really just don’t know
Answer:
15
Step-by-step explanation:
Because the two triangles are similar:
[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]
Hope this helps!
Which expression is equivalent to 4+2(1+3x)
Answer:
I'm glad you asked!
Step-by-step explanation:
OK,let's simplify the number for a equivalent expression.
[tex]4+2(1+3x)[/tex]
Distribute:
[tex]=4+(2)(1)+(2)(3x)[/tex]
[tex]= 4+2+6x[/tex]
Combine Like Terms:
[tex]=4+2+6x[/tex]
[tex]=(6x)+(4+2)[/tex]
[tex]=6x+6[/tex]
The Final Answer is : [tex]6x+6[/tex]
The expression that is equivalent to 4+2(1+3x) is 6x+6.
What is an Algebraic expression?Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.
How do simplify the algebraic expression?Given, 4+2(1+3x)
Firstly distribute 2(1+3x) to get 2+6x then,
4+2(1+3x)
=4+2+6x
=6x+6
Thus, 4+2(1+3x)=6x+6
For more simplification visit- https://brainly.com/question/953809?referrer=searchResults
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What is the measure of angle L in parallelogrami LMNO?
20°
30°
40°
50°
Answer:
40°
Step-by-step explanation:
2x = 3x - 20 add like terms
x = 20 and angle l is equal to 3x minus 20 so 3 × 20 - 20 = 40°
PLEASE HALP ME! ( WILL MARK BRAINLIEST! Thank you! ;)
Answer: 1/20
Step-by-step explanation:
Decimal Fraction Percentage
0.05 1/20 5%
The Sky Train from the terminal to the rental car and longterm parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. What is the average waiting time (in minutes)
Answer:
Average waiting time = 4 minutes
Step-by-step explanation:
From this question, we are told that the sky train is supposed to arrive every 8 minutes.
Thus, the waiting time of the passengers for the train = 8 minutes.
Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.
So, average waiting time = 50% × 8
Average waiting time = 4 minutes
what is Associative propert
Answer:
Associative property of multiplication is the grouping of numbers being multiplied can be changed without affecting the product.
here is an example!
Addison Rae work using the associative property:
(-8.5)(5)(-4) =
(-8.5)(-20) =
170
hope this helped it was from my FLVS schooling :)
Find and of the function = − −( − ).
Answer:
Thats not possible
Step-by-step explanation:
There is no:
numbersvariablesonly negative signsLet the velocity of a particle be given by v(t) = 2t+a.(a) Find the number a such that the average value of v(t) on the interval [0,1] is -2.(b) Using v(t) from part (a), find the distance traveled by the particle during the time period from [0,4].
Answer:
The velocity is v(t) = 2*t + a
a) we want to find the average velocity betwen t = 0 and t = 1.
We can do this as:
Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a
b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.
For this we can see the integral:
[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]
Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. T(X1,X2,X3,X4) = (x1 +4x2, 0, 3x2 +x4, x2 -x4)
The transformation matrix for the mapping T is the matrix T such that
[tex]\mathbf T(\vec x)=T\,\vec x[/tex]
where
[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]
The correct matrix A is
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)
By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.
The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.
Thus, the matrix A that implements the mapping T is:
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
Learn more about linear transformation here:
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2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
Simplify [tex]4(y+11)2-3y^2[/tex]
Answer:
[tex]y^2+88y+484[/tex]
Step-by-step explanation:
[tex]4(y+11)^2-3y^2= \\\\4(y^2+22y+121)-3y^2= \\\\4y^2-3y^2+88y+484= \\\\y^2+88y+484[/tex]
Hope this helps!
which is composite number?
Answer:
A whole number that can be made by multiplying other whole numbers.
Example: 18 can be made by 3 × 6 so is a composite number.
16 can be made by 4 x 4 so it is a square root and a composite number
14 can be made by 2 x 7 so is is a composite number.
It is not a prime number as all Composite Number have factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,
Answer:
We need to examine the natural numbers.
The natural numbers are the counting numbers,
1, 2, 3, 4, 5, 6, ...
The number 1 is neither prime nor composite.
All natural numbers greater than 1 are either prime or composite.
A prime number is a number that has exactly two factors, itself and 1.
A composite number has more than 2 factors.
A composite number is a natural number greater than 2 that is not a prime number.
Examples:
Prime: 2, 3, 5, 7, 11, ...
Composite: 4, 6, 8, 9, 10, 12, ...
Jaleel and Lisa are simplifying the expression 2(x-2) + 2 as shown
Answer:
Jaleel is correct because 2 (x + 2) = 2x - 4
Step-by-step explanation:
To solve 2 (x - 2) + 2:
2 (x - 2) + 2
Distribute
2x - 4 + 2
Combine like terms
2x - 2
Lisa did not distribute correctly :)
Answer:
D
Step-by-step explanation:
NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned. If a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is:
Answer:
The required probability is 0.4828.
Step-by-step explanation:
We are given that a company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B.
Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned.
Let the probability that production is of Type A = P(A) = 30%
Probability that production is of Type B = P(B) = 1 - P(A) = 1 - 0.30 = 70%
Also, let R = event that pair of goggles are returned
So, the probability that type A goggles are returned within 10 days after the sale = P(R/A) = 5%
Probability that type B goggles are returned within 10 days after the sale = P(R/B) = 2%
Now, given a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is given by = P(B/R)
We will use the concept of Bayes' Theorem to calculate the above probability.
So, P(B/R) = [tex]\frac{P(B) \times P(R/B)}{P(A) \times P(R/A)+P(B) \times P(R/B)}[/tex]
= [tex]\frac{0.70 \times 0.02}{0.30 \times 0.05+0.70 \times 0.02}[/tex]
= [tex]\frac{0.014}{0.029}[/tex] = 0.4828
In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
According to a recent study, annual per capita consumption of milk in the United States is 23.8 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered below. Use the data to test your hypothesis.
a. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.
b. What is a point estimate of the difference between mean annual consumption in Webster City and the national mean? (2 decimals)
c. At α=0.01
test for a significant difference by completing the following.
Calculate the value of the test statistic (2 decimals).
The p-value is _____ (4 decimals).
Reject the null hypothesis?
27.8
23.84
25.25
21
17.52
19.61
19.83
26.18
34.97
30
28.59
20.57
26.94
27.24
Answer:
a. In the explanation.
b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:
[tex]d=M-\mu=24.95-23.8=1.15[/tex]
c. Test statistic t = 0.90
P-value = 0.1932
The null hypothesis failed to be rejected.
Step-by-step explanation:
We have a sample, wich mean and standard deviation are calculated as:
[tex]M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8[/tex]
This is a hypothesis test for the population mean.
The claim is that the consumption of milk in the Midwest is significantly higher than the national average.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=23.8\\\\H_a:\mu> 23.8[/tex]
The significance level is 0.01.
The sample has a size n=14.
The sample mean is M=24.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=14-1=13[/tex]
This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>0.9)=0.1932[/tex]
As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.
