Answer:
H0:p= 0.80 H1: p< 0.80 one tailed test
Step-by-step explanation:
We state the null and alternative hypotheses as that the results are 80 % against the claim that the results are less than 80%.
H0:p= 0.80 H1: p< 0.80 one tailed test
p2= 0.8 , p1= 74/97= 0.763
q1= 1-0.763= 0.237 q2= 0.2
The level of significance is 0.05 .
The Z∝= ±1.645 for ∝= 0.05
The test statistic used here is
Z= p1-p2/ √pq/n
Putting the values:
Z= 0.763 -0.8 / √ 0.8*0.2/97
z= -0.037/ 0.0406
z= -0.9113
The Z∝ = ±1.645 for ∝= 0.05 for one tailed test.
As the calculated value does not fall in the critical region we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that such polygraph results are correct less than 80% of the time.
Using the normal probability table.
P (Z < -0.9113)= 1- P(z= 0.9311) = 1- 0.8238= 0.1762
If P- value is smaller than the significance level reject H0.
0.1762> 0.005 Fail to reject H0.
The weight load on an airplane pallet is normally distributed with a mean of 250 pounds and a standard deviation of 40 pounds. What is the probability that a randomly selected pallet will support more than 290 pounds
Answer: 0.1587
Step-by-step explanation:
Given : The weight load on an airplane pallet is normally distributed with a mean of 250 pounds and a standard deviation of 40 pounds.
i.e. [tex]\mu = 250[/tex] pounds
[tex]\sigma=40[/tex] pounds
Let x be the weight load on an airplane pallet.
Then, the probability that a randomly selected pallet will support more than 290 pounds will be :-
[tex]P(X>290)=P(\dfrac{X-\mu}{\sigma}>\dfrac{290-250}{40})\\\\=P(Z>1)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1)\\\\=1-0.8413\ \ \ \ [\text{by z-table}]\\\\=0.1587[/tex]
Hence, the required probability is 0.1587 .
Add the following polynomials (write answers in descending order):
1. (7j9 – 2) + (5j9 - j - 3)
2. (8a - 4) + (3a + a - 2)
3. (6m² + 1) + (3a + a - 2)
4. (3m + 1) + (9m + 3m - 2)
5. (- 5x2 - x + 4) + (- 3x?
5x + 2)
Answer/Step-by-step explanation:
1. (7j³ - 2) + (5j³ - j - 3)
Open the parentheses
7j³ - 2 + 5j³ - j - 3
Collect like terms. Like terms are terms that have the same degree.
7j³ + 5j³ - j - 2 - 3 (7j³ and 5j³, have the same degree, 2 and 3 are if the same degree)
12j³ - j - 5 (this already in descending order)
2. (8a⁵ - 4) + (3a⁵ + a - 2)
Open parentheses
8a⁵ - 4 + 3a⁵ + a - 2
Collect like terms
8a⁵ + 3a⁵ + a - 4 - 2
12a⁵ + a - 6 (in ascending order from largest to smallest degree)
3. (6m² + 1) + (3a⁵ + a - 2)
6m² + 1 + 3a⁵ + a - 2
Collect like terms
6m² + 3a⁵ + a + 1 - 2
6m² + 3a⁵ + a - 1
Rearrange from largest to smallest degree
3a⁵ + 6m² + a - 1
4. (3m⁵ + 1) + (9m⁵ + 3m - 2)
3m⁵ + 1 + 9m⁵ + 3m - 2
Collect like terms
3m⁵ + 9m⁵ + 3m + 1 - 2
12m⁵ + 3m - 1
5. (- 5x² - x + 4) + (- 3x² - 5x + 2)
Open parentheses
-5x² - x + 4 - 3x² - 5x + 2
Collect like terms
-5x² - 3x² - x - 5x + 4 + 2
-8x² - 6x + 6
Prove the multiple of two consecutive integers is positive
Answer:
2×3=6
or 6×5=30
Step-by-step explanation:
Theres a lot!
1+tanA.tan2A = sec2A
Answer:
Step-by-step explanation:
1+tan2A(tanA)=sec2A
Right hand side
sec2A=1cos2A=1cos2A−sin2A
=cos2A+sin2Acos2A−sin2A
=1+tan2A1−tan2A
=1−tan2A+2tan2A1−tan2A
=1−tan2A1−tan2A+2tan2A1−tan2A
=1+2tanA1−tan2A×tanA
=1+tan2A×tanA
=Left hand side
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6 + x is an example of _____. a formula a constant a variable an expression
Answer:
it is an example of an expression
Step-by-step explanation:
it is an example of an expression because it is asking a question without an equal sign. so its not a question, but an expression
(10c^6d^-5)(2c^-5d^4)
Answer:
The value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].
Step-by-step explanation:
In this problem, we need to evaluate [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex]. Here, c and d are variable with exponents.
Taking both c together
[tex]=(10c^6{\cdot} 2c^{-5})\\\\=20(c^6{\cdot} c^{-5})\\\\=20c^{6-5}\\\\=20[/tex]
Taking both d together
[tex]=(d^{-5}{\cdot}d^4)\\\\=d^{-5+4}\\\\=d^{-1}[/tex]
So,
[tex](10c^6d^{-5})(2c^{-5} d^4)=20d^{-1}[/tex]
Hence, the value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].
describe how to obtain the graph of the transformed function below from its parent function.
Answer:
shifted horizontally to the right 4 units, then stretched vertically by a factor of "3" , and finally shifted vertically up 6 units.
Step-by-step explanation:
Given the function
[tex]f(x)=\frac{3}{x-4} +6[/tex]
we can say that its parent function
[tex]f(x)=\frac{1}{x}[/tex]
was:
shifted horizontally to the right 4 units (given by the 4 units subtracted from the variable x)
stretched vertically by a factor of "3"
and finally shifted vertically up 6 units.
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wats to determine how many houses the carrier can deliver in 7.5 minutes at the rate. He thiks that to find the awnsers, he should do the following: 1. Divide 36 houses by 30 to find a unit rate of 1.2 houses per minute 2. Then multiply 1.2 houses per minute minute by 7.5 to get 9 houses.
Answer:
he interval itself is either correct in its estimate [i.e. the true parameter value is in ... year, and then interviews all students in that class, the sampling method is a ... If the target population is all U.S. adults, then a telephone directory would not
Step-by-step explanation:
Super Saver grocery carries a 128 ounce jug of iced tea. The nutrition label states that the jug serves 16 people. Which rate best represents the relationship between the number of ounces of iced tea and the number of servings? F. 8 ounces per serving G. 16 servings per ounce H. 128 ounces per serving J. 8 servings per ounce
Answer:
I am pretty sure it is J
Step-by-step explanation:
128 divided by 16 equals 8
Answer:
F
8 ounce per serving
Step-by-step explanation:
128 ounce jug of iced tea.
label says = serves 16 people
therefore, the number of ounces per serving = 128 ounce / 16 serving
= 8 ounce per serving
so the answer is option F
The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 8 minutes.
(a) Find the probability that the time interval between two successive barges is less than 5 minutes.
(b) Find a time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t.
Answer:
a) 0.4647
b) 24.6 secs
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = 0.4647
Therefore the probability that the time interval between two successive barges is less than 5 minutes is 0.4647
b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = 24.6 secs
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is 24.6 secs
a.) we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.
b.) the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.
Given to us:
exponential distribution with mean = E(T) = 8,
The mean of the exponential
E(T) = 1/λ
1/λ = 8
λ = 1/8
∴ [tex]t(t) =\frac{1}{8} \times e^\frac{-t}{8} }\ ;\ [ t > 0][/tex]
(a) The probability that the time interval between two successive barges is less than 5 minutes.
Now the probability we need
[tex]\begin{aligned} \ [T<5] &= \int\limits^5_0 {t(t)} \, dt\\&= \int\limits^5_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\\\&= [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^5\\&= - [ e^{-t/8}]_0^5\\&= - [ e^{-5/8} - 1 ]\\&= 1 - e^{-5/8}\\&= 0.4647\end{aligned}[/tex]
So, we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.
b) Now we find t such that;
[tex]\begin{aligned} \ &p[T>t]=0.95\\ & \int\limits^{10}_0 {t(t)} \, dt=0.95\\& \int\limits^{10}_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt=0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt = 0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt=0.95 \\\\& [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^{10}=0.95\\\\& - [ 0 - e^{-t/8} ] = 0.95&\ \ e^{-t/8} = 0.95\\\end{aligned}[/tex]
taking logs,
t = 24.6 secs
Hence,the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.
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A researcher measures the correlation between the frequency of self-esteem (high,low)and health status (lean/healthy,overweight/obese).Based on the frequencies for each nominal category given below,what is the value of the phi correlation coefficient?img Health status Lean/Healthy Overweight/ ObeseSelf Esteem Low 18 32 High 32 18
A) 0.08
B) 0.28
C) 0.52
D) 0.56
Answer: B) 0.28
Step-by-step explanation:
Given that:
Lean/Healthy Overweight/ ObeseSelf Esteem Low 18 32 High 32 18
Overweight/Obese Lean/Healthy Total
Low 32 18 50
High 18 32 50
Total 50 50 100
the phi correlation coefficient is defined by Ф = √x²/n
where n = 100 ( total number of response )
x² = [(32×32 - 18×18)² × 100] / [50 × 50 × 50 × 50]
Ф = √ [(700)² x 100) / (50)⁴ × 100
Ф = 700 / 50²
Ф = 0.28
Therefore option B) is the correct answer
A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of probability.
Answer: Experimental probability
Step-by-step explanation:
There are two kinds of probability: Theoretical probability and Experimental probability.
To calculate theoretical probability we divide favorable outcomes by total outcomes.
To calculate experimental probability we divide number of times an event occurs by the total number of trials or times the activity is performed.
Here, A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, which is dependent on the activity he performed, thus it is an experimental probability.
the population of butterflies in a particular place is 50. if population increases by 20% in every 6 months . find out the population of butterflies after 1 year
Answer:
butterflies (b)=50
butterflies in 6 months =20/100×50=10+b =60
butterflies in 12 months =2(6months)
butterflies in 12 months= 120
The population of butterflies after 1 year is 72 butterflies
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the present population of butterflies be A = 50 butterflies
The percentage increase after 6 months = 20 %
The population of butterflies after 6 months = present population of butterflies + percentage increase after 6 months
The population of butterflies after 6 months = 50 + ( 20/100 ) x 50
= 50 + ( 0.2 x 50 )
= 50 + 10
= 60 butterflies
The population after 6 more months = population of butterflies after 6 months + percentage increase after 6 months
The population after 6 more months = 60 + ( 20/100 ) x 60
= 60 + 0.2 x 60
= 60 + 12
= 72 butterflies
Hence , The population of butterflies after 1 year is 72 butterflies
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You and your six friends are eating lunch and decide to split the bill equally. Write an algebraic expression explaining how you will pay the bill.
jonalyn has five discs, each with a different counting numbers printed on one face. however , she lost three discs and all she can remember is that the sum of the five numbers is 50 and the number in the two remaining discs are 12 and 9. 1. what is the greatest possible value of one of the numbers? 2. what can be the possible values of the three other numbers?
Answer: (1) 26 (2) 1, 3, 25
Step-by-step explanation:
Let a, b, and c represent the three discs.
a + b + c + 12 + 9 = 50
a + b + c = 29
1) Since a, b, and c are all different numbers then the one possibility is:
a = 1, b = 2, --> c = 26
2) There are many different possibilities for creating a sum of three numbers whose total is 29.
One example is provided above in #1.
Here are few other examples:
1, 3, 25 2, 3, 24 3, 4, 19 4, 5, 20
1, 4, 24 2, 4, 23 3, 5, 18 4, 6, 19
1, 5, 23 2, 5, 22 3, 6, 17 4, 7, 18
Using a system of equations, it is found that:
The greatest possible value of one of the numbers is 26.The possible values are all values of x,y and z different of 12 and 9 such that:[tex]x + y + z = 29[/tex]
---------------------
There are 5 distinct numbers, with a sum of 50, thus they are:[tex]x + y + z + t + w = 50[/tex]
Two of them are 12 and 9, thus [tex]t = 9, w = 12[/tex], and:[tex]x + y + z + 9 + 12 = 50[/tex]
[tex]x + y + z + 21 = 50[/tex]
[tex]x + y + z = 29[/tex]
The greatest possible value of one of the numbers is 26, as then one would be 2 and the other 1, having five distinct numbers.The possible values are all values of x,y and z different of 12 and 9 such that:[tex]x + y + z = 29[/tex]
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Find the number that completes each of the following proportions: a.8120=4c b.n0.5=0.71 c.8x=23 d. 7:6=k:120
Answer:
a. c = 2030,
b. n = 1.42,
c. x = 2.875,
d. k = 140
Step-by-step explanation:
a ) 8120 = 4c,
c = 8120 / 4 = 2030
b ) 0.5n = 0.71,
n = 0.71 / 0.5 = 1.42
c ) 8x = 23,
x = 23 / 8 = 2.875
d ) 7 : 6 = k : 120
Here we want to convert this ratio into fraction form,
7 / 6 = k / 120
And now we can cross - multiply to determine the value of k,
6k = 7(120) = 840,
k = 840 / 6 = 140
We can check the value of k, by plugging it back into our ratio, and see if it reduces to 7 : 6,
140 : 120,
14 : 12,
7 : 6
20 girls tried out for the basketball team and 18 boys tried out. What was the ratio of girls to boys who tried out for the team?
Answer: 10 : 9
Step-by-step explanation:
GIVEN
20 girls tried out
18 boys tried out
----------------------------------------------
The final ratio should be girl to boy
girl to boy
=20 : 18
=10 : 9 ⇔ divide 2 on both sides (simplify the ratio)
Hope this helps!! :)
Please let me know if you have any question
what is 8/9 minus 1/3
Answer: Hi!
Your answer is 5/9.
Step-by-step explanation:
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 8 by 3, and get 24.
Then we multiply 1 by 9, and get 9.
Next we give both terms new denominators -- 9 × 3 = 27.
So now our fractions look like this:
24/27 - 9/27
Since our denominators match, we can subtract the numerators.
24 − 9 = 15
So the answer is:
15/27
(After you simplify it, it will be 5/9.)
Hope this helps!
The value of the expression "8/9 minus 1/3" is 5/9.
To subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 9 and 3 is 9.
We can convert both fractions to have a denominator of 9:
(8/9) - (1/3)
Multiplying the numerator and denominator of the first fraction by 3, we get:
(8/9) - (1/3)
This gives us:
8/9 - 1/3
Since both fractions now have a common denominator of 27, we can subtract the numerators:
(8 - 3x 1) / 9
= (8-3)/9
= 5/9.
Therefore, 8/9 minus 1/3 is equal to 5/9.
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3. An electric bill is an essential expense for young people who get their first
apartment. The following is a list of Jordan's monthly electric bills for the past
10 months.
$115,
$150, $144, $126, $90, $90, $95, $110, $120, $88
Round your answers to the nearest cent.
a. What is the mean monthly electric bill?
b. What is the range?
c. What is the variance?
d. What is the standard deviation?
Answer:
Mean = $123.8
Range= $72
Variance= $607.344
Standard deviation=$ 24.64
Step by step explanation:
The list of the data of electricity bill on ascending order
$88,$90,$90,$95,$110,$115,$120,$126,$144,$150
Mean = (summation of($88,$90,$90,$95,$110,$115,$120,$126,$144,$150))/10
Mean = 1238/10
Mean = $123.8
Range= highest value- Lowest VA
Range= 150-88
Range= $72
Variance=( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)/10
Variance= (1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)/10
Variance= 6073.44/10
Variance=$ 607.344
Standard deviation= √variance
Standard deviation= √ 607.344
Standard deviation=$ 24.64
The mean monthly electric bill is $123.8
The Range is $72
The variance is $607.344
The standard deviation is $ 24.64
What is the arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
Σx = 88+90+90+95+110+115+120+126+144+150
Σx = 1238
Here n = 10
⇒ Mean = Σx/n
⇒ Mean = 1238/10
⇒ Mean = $123.8
Hence, the mean monthly electric bill is $123.8
⇒ Range = Largest value - Least value
⇒ Range = 150-88
⇒ Range= $72
Hence, the Range is $72
⇒ Σ(x -mean)² = ( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)
⇒ Σ(x -mean)² =(1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)
⇒ Σ(x -mean)² = 6073.44
Here n = 10
⇒ Variance = Σ(x -mean)²/10
⇒ Variance = 6073.44/10
⇒ Variance = $607.344
⇒ Standard deviation = √variance
⇒ Standard deviation = √607.344
⇒ Standard deviation = $24.64
Hence, the standard deviation is $24.64.
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Solve the Multi-Step Equations and check. Solve for x
15x - 24 - 4x = -79
Answer:
x = -5
Step-by-step explanation:
Step 1: Write out equation
15x - 24 - 4x = -79
Step 2: Combine like terms
11x - 24 = -79
Step 3: Add 24 to both sides
11x = -55
Step 4: Divide both sides by 11
x = -5
Step 5: Check step
Plug in -5 into the original equation
15(-5) - 24 - 4(-5) = -79
-75 - 24 + 20 = -79
-99 + 20 = -79
-79 = -79
Answer:
x = -5
Step-by-step explanation:
15x - 24 - 4x = -79
11x - 24 = -79
11x = -55
x = -5
Check:
15 * -5 - 24 - 4 * -5
= -75 - 24 + 20
= -79
does someone know the answer of (-9+v)/8=3
Hi
(-9+V) /8 = 3
-9/8 +V/8 = 24/8
-9+V = 24
V = 24+9
V = 33
let's check : -9+33 = 24 and 24/8 = 3
solve | − 9 | − | − 4 | =
Answer: 5
Step-by-step explanation:
First of all, keep in mind that absolute value of any real number (positive and negative) is always positive because it stands for the distance from zero, and distance will never be negative.
i.e. |x|=x, |-x|=x
-------------------------------------------
|-9|-|-4|
=9-4
=5
Hope this helps!! :)
Answer:
[tex]\huge \boxed{5}[/tex]
Step-by-step explanation:
[tex]|-9|-|-4|[/tex]
Apply rule : [tex]|-a|=a[/tex]
[tex]9-4[/tex]
Subtract.
[tex]=5[/tex]
6-7 Please help BRAINLEST!
Answer:
18
Step-by-step explanation:
25=7+r 25-7=18 7-7=0
r=18 Do you understand? I really hoped I helped. I was in your position when i was learning that.
What is the domain of this function?
will mark brainliest and give 50 points pls help asap tyyy <3
Answer: 20, -7, and -3
Step-by-step explanation:
`1.) 15 plus 8 is 23
23 minus 3 equals 20
2.) -25 plus 5 equals -20
-20 plus 13 is -7
3.) i can see the last one to show work
Translate the figure 4 units right and 2 units up.
Draw a vector from the origin 4 units right and 2 units up.
Answer:
Hey there!
The correct answer would be a line from the point (0, 0) to the point (4, 2).
Let me know if this helps :)
anyone know this one
Answer:
A e/f
Step-by-step explanation:
[tex]\frac{-e}{-f} = \frac{e}{f}[/tex]
Two negatives always equal one positive
Recall:
Negative + Negative = Positive
Negative + Positive = Negative
Positive + Positive = Positive
If f(x)=1-x^2+x^3, then f(-1)=
Answer:
Well, we know that there exists a function f(x) such that f(x-1) is a direct transformation of its parent function. First we want to set x=x-1. Conceptually, it might be easier just to annotate one of the x’s as a completely different variable, because we know that x doesn’t equal x-1. So let’s rewrite as x=y-1 and solve for y.
We now have y=x+1 where y(x) is actually our parent function and y(x)=f(x+1). So take our equation f(x-1) and substitute each x with (x+1). So f(x)=2(x+1) + 3
f(x)= 2x + 5. We can check this by finding f(x-1) because it should equal 2x+3.
f(x-1)= 2(x-1) + 5
f(x-1)= 2x + 3.
Hoped I helped
To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33. If the sample has a standard deviation of s = 9, do we reject or accept the null hypothesis using a two-tailed test with alpha = .05?
Answer:
Yes we reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 9[/tex]
The population mean is [tex]\mu = 40[/tex]
The sample mean is [tex]\= x = 33[/tex]
The standard deviation is [tex]\sigma = 9[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
For a two-tailed test
The null hypothesis is [tex]H_o : \mu = 40[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 40[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 33 - 40 }{ \frac{9}{\sqrt{9} } }[/tex]
=> [tex]t = -2.33[/tex]
The p-value for the two-tailed test is mathematically represented as
[tex]p-value = 2 P(z > |-2.33|)[/tex]
From the z-table
[tex]P(z > |-2.33|) = 0.01[/tex]
[tex]p-value = 2 * 0.01[/tex]
[tex]p-value = 0.02[/tex]
Given that [tex]p-value < \alpha[/tex] Then we reject the null hypothesis
Michaela has h hair ties. Michaela's sister has triple the number of hair ties that Michaela has . Choose the expression
that shows how many hair bows Michaela's sister has.
A. H^3
B. 3/H
C. H/3
D. 3H
Answer:
D
Step-by-step explanation:
Triple means 3 times something. "Times" means multiplication and the "something" is h so the answer is 3 * h = 3h.