Answer:
D
Step-by-step explanation:
because i took the test
Answer:
Option D: (9,3)
Step-by-step explanation:
Please Help, Math Problem.....
Answer:
Answer is given below with explanations.
Step-by-step explanation:
Given that triangle ABC is similar to triangle PQR
Then
Angle A is congruent to Angle PAngle B is congruent to Angle QAngle C is congruent to Angle RLine segment AB is congruent to Line segment PQLine segment BC is congruent to Line segment QRLine segment AC is congruent to Line segment PR .
THEN THE CORRECT OPTIONS ARE
OPTION D) AND
OPTION E)
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Find the mode of the following data:
18, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20
O A. 13
OB. 10
O c. 16
D. 14
SUBMIT
10..................
The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. x 0 1 2 3 4 5 P(x) 0.09 0.26 0.29 0.20 0.09 0.07 Find P(2 or fewer).
Answer:
probability (x ≤2) = 0.64
Step-by-step explanation:
P(2 or fewer) = probability of 2 or fewer
probability of (2 or fewer) = probability (x ≤2)
probability of (2 or fewer) = probability when x is 0 + probability when x is 1 + probability when x is 2
probability of (2 or fewer) = probability (x =0) + probability of (x =1 ) + probability (x= 2)
probability of (x=0) = 0.09
probability of (x=1) = 0.26
probability of (x =2) = 0.29
probability of (2 or fewer) = 0.09 + 0.26 + 0.29 = 0.64
probability (2 or fewer) = probability (x ≤2) = 0.64
Answer:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
Step-by-step explanation:
For this case we have the following probability distribution:
x 0 1 2 3 4 5
P(x) 0.09 0.26 0.29 0.20 0.09 0.07
And we want to find the following probability:
[tex] P(X \leq 2)[/tex]
And we can find the probability like this:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
An aquarium holds 11.08 cubic feet of water,and is 2.5 feet long 1.3 feet wide.what is its depth.Round your answer to the nearest whole number.
Answer:
3ft
Step-by-step explanation:
volume = l*w*h
To solve use what you know.
11.08 ft^3 = 2.5 ft * 1.3 ft * X ft
2.5 ft *1.3 ft =3.5 ft^2
11.08ft^3 / 3.5ft^2 = 3.409 ft
nearest whole number is 3 ft
Please answer this correctly
To get the volume, you need the area of the sides of the square.
The total surface area is 96, with 6 sides. To get the surface area of just one side, divide 96 by 6, which gets you 16. The surface area of a single square is 16. To get one side of the square, divide that by 4 because there are 4 sides.
Now, multiply 16 by 4 to get the volume.
The volume is 64 cubed milllimeters.
brainlieest?
Also i hope this helped
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find:
Chapter Reference
b
Surface area of the pyramid
Answer:
228 cm²
Step-by-step explanation:
The base of the pyramid is a regular quadrilateral (a square), so there are 4 congruent lateral faces.
The total surface area is therefore:
A = 36 cm² + 4 (48 cm²)
A = 228 cm²
A farmer has a total of 21 cows and chickens altogether The animals have 54 legs how many cows and how many chickens does the farmer have?
Answer:
The farmer has 4 cows and 15 chickens.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of cows
y is the number of chickens.
A farmer has a total of 21 cows and chickens altogether
This means that x + y = 21.
The animals have 54 legs
A cow has four legs, while a chicken has 2 legs. So
4x + 2y = 54.
From the first equation:
y = 21 - x
Replacing
4x + 2(21 - x) = 54
4x + 42 - 2x = 54
2x = 12
x = 6
y = 21 - x = 21 - 6 = 15
The farmer has 4 cows and 15 chickens.
Exercise #1: The amount of money in Nicole's bank account can be represented by the function f(x) = 32.50x + 200,
where f(x) is the amount of money in dollars after x days. State the meaning of the slope and y-intercept of this function in
the given context
Sue has 2 cats. Each cat eats of a tin of cat food each day. Sue buys 8 tins of cat food. Has Sue bought enough cat food to feed her 2 cats for 14 days? You must show how you get your answer.
Answer:
Each cat eats a tin each day. It means 2 tins are required each day for both the cats. So, for 14 days, they will need 28 tins.
Sue has bought just 8 tins, which is not enough
PLZ HURRRY!!!!! What is the circumference of the circle
Answer:
40.192
Step-by-step explanation:
C=D(pi)
D=6.2*2
C=12.8*3.12
C=40.192
Answer:40.192
Step-by-step explanation:the formula for a circumference if a circle is C=2•3.14•r^2 fill in for r and calculate for your answer
which of the following options is an odd function?
Answer: The answer is C
Step-by-step explanation:
what is a random variable
Answer:
Check Below.
Step-by-step explanation:
In Probability/ Statistics in simple terms it is a variable which possess the following characteristics within a sample space: 1) Their values are defined within the set of Real Numbers, i.e. it is a Quantitative variable. 2) It is possible to calculate its probability.
Can someone please help me with this? What would be the measure of angle R to the nearest tenth?
Answer:
Step-by-step explanation:
There are two ways to do this.
1. You could make an accurate diagram and measure R. This works but the computer won't like it. However you will know if you are correct. An answer ± 2 degrees would tell you that you are likely correct.
2. The second way is to find <C. Similarity guarantees that <C and <R are equal. The adjacent side to angle C is the second longest line. The second longest line in PQR is the adjacent side of <R.
Naturally we will use the second method, but you ought to try the first method. It's cumbersome but it will teach you how to read the values of triangles to make clear the trig functions.
Tan(C) = opposite over adjacent
Tan(C) = 7 / 9
Tan(C) = .77777777...
<C = tan-1(0.7777777...)
<C = 37.87
<C = 37.9
6.
The city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
cost
Last month, one homeowner used 1,600 gallons. Write 1,600 gallons in terms of hundred gallons.
hundred gallons
What is the homeowner's total cost in dollars) for water last month?
$
The homeowner received a bill for $13.36. Was the billing correct?
Yes
Or No
Answer:
cost in term of w is
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46*16 +3 = 10.36 dollars
no
Step-by-step explanation:
The cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
The equation will be written as:-
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46 x 16 +3 = 10.36 dollars
Therefore, the cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
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When 893893 male workers were asked how many hours they worked in the previous week, the mean was 45.645.6 with a standard deviation of 14.614.6. Does this suggest that the population mean work week for men exceeds 4040 hours? Answer by completing parts (a) through (d).
Answer:
a) A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b) Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c) [tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d) Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
Step-by-step explanation:
Information provided
[tex]\bar X=45.6[/tex] represent the sample mean
[tex]s=14.6[/tex] represent the sample standard deviation
[tex]n=893[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
a. Identify the relevant and parameter variable. Choose the correct relevant variable below.
A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b. State the null and alternative hypotheses. State the null hypothesis.
We want to verify if the population mean is higher than 40, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c. Calculate the statistic
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d. Conclusion
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
A probability model for rolling a cube with faces numbered 1 through 6 is:
Answer:
P(a)= Your desired outcome / The number of real outcomes.
Step-by-step explanation:
Ex. Probability model for rolling a 1 on a 6 sided die -
1 (desired outcome) / 6 (Number of real outcomes)
Let me know if you need more help!
A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. (a) List all possible two-course selections. (b) Comment on the likelihood that EPR 646 and EPR 679 will be selected.
Answer:
A) A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program.
The courses were not listed, but let's assume the courses are:
EPR 646,
EPR 602
EPR 679
EPR 622
EPR 684
In this case, we can see there are 5 possible courses.
Selecting them:
[tex]^5C_2 = \frac{5*4*3*2*1}{2*(5-2)!} = 10[/tex]
Therefore, there are 10 selections.
All possible two course selections:
(622,602); (622, 684); (622, 679); (622, 646); (646, 602); (646, 679)
(646,684); (602, 684); (602, 679);
(679, 684)
b) Likelihood that EPR 646 and EPR 679 will be selected
From the data abeve, EPR 646 and EPR 679 can be selected just once.
Therefore, the likelihood =
P(selecting EPR 646 and EPR 679) = [tex]\frac{num. of . times. event. occured}{total. number. of. outcome} =\frac{1}{10}[/tex]
Likelihood that EPR 646 and EPR 679 will be selected is [tex]\frac{1}{10}[/tex] = 0.1
Answer:A student entering a doctoral program in educational psychology is required to select courses from the list of courses provided as part of his or her program.
(a) List all possible -course selections.
(b) Comment on the likelihood that will be selected
Step-by-step explanation:
8 x 10^3 is how many times as large as 4 x 10^2?
8 * 10^3 is larger than 4 * 10^2
10*10*10 = 1000 * 8 = 8000
10*10= 100 * 4 = 400
A camp counselor and six campers are to be seated along a picnic bench. In how many ways could this be done if the counselor occupies the seat in the middle and the camper who tends to start food fights sits next to him (either on the left or on the right)
Answer:
This can be done in 240 ways.
Step-by-step explanation:
Number of arrangments:
The possible number of arrangments of n elements is given by the following formula:
[tex]A_{n} = n![/tex]
In this question:
7 people(camp counselor and six campers).
Camp counselor in the middle.
Camper who start food fights either to his left or to his right. For each of these cases, the other 5 campers are arranged in 5 positions. Then
How many ways:
[tex]T = 2A_{5} = 2*(5!) = 240[/tex]
This can be done in 240 ways.
A study by Consumer Reports showed that 64% of supermarket shoppers believesupermarket brands to be as good as national brands. A manager of a local storebelieves that the percentage is higher in his store. She asks a random sample of145 shoppers whether they believed that supermarket brand ketchup was as goodas the national brand ketchup. Out of the 145 shoppers asked, 89 believed the supermarket brand was as good as the national brand. Use α= 0.05 significancelevel and conduct a hypothesis test.
Answer:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
Step-by-step explanation:
Information given
n=145 represent the random sample taken
X=89 represent the number of people who believed the supermarket brand was as good as the national brand
[tex]\hat p=\frac{89}{145}=0.614[/tex] estimated proportion of people who believed the supermarket brand was as good as the national brand
[tex]p_o=0.64[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true proportion is less than 0.64, the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.64[/tex]
Alternative hypothesis:[tex]p < 0.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
5)
Calculate the ratio to the nearest hundredth.
-
RATIO
U
DIAMETER (d) CIRCUMFERENCE (C)
20 in.
62.83 in.
är
liliom
DE
10 in.
31.41 in.
6
in.
18.84 in.
2
in.
6.28 in.
1
in.
3.14 in.
0
-
Complete
A
16% Complete
earch
'o
e
Answer:
Answer for (a) to (e) = 0.32
Calculate the ratio to the nearest hundredth.
Find the Ratio of Diameter (d) and circumference (C)
Step by step explanation:
In order to determine the ratio we must know the formula for the circumference of a circle. Then relate it to the diameter.
But since we have been the value if both circumference and diameter, we would just calculate the ratio.
Circumference of a circle = 2πr
Where d = diameter = 2r
Circumference = πd
a) d = 20 in.
C = 62.83 in.
Ratio of Diameter (d) and circumference (C) = d:C
= 20/(62.83)
d:C = 0.32
b) d=10 in.
C =31.41 in.
d:C = 10/(31.41)
d:C = 0.32
c) d =6 in.
C =18.84 in.
d:C = 6/(18.84)
d:C = 0.32
d) d= 2 in.
C = 6.28 in.
d:C = 2/6.28
d:C = 0.32
e) d = 1 in.
C = 3.14 in.
d:C = 1/3.14
d:C = 0.32
The above answers indicate that the ratio of a circumference of a circle to its diameter = d/C = d/(π×d)
= 1/π = 0.32
Evaluate this power with a base that is a negative fraction.
(−1
4
)2
Answer:
(16)^-1 or (4)^-2
Step-by-step explanation:
(-1/4)^2, we can convert this to (1/16), which is (16)^-1 or (4)^-2.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]-\frac{1}{4} ^{2}[/tex]
[tex]\frac{-1^{2} }{4^{2} }[/tex]
[tex]=\frac{1}{16}[/tex]
the little boxes on the bottom with the numbers in it are the answers. plz do all three if u can
Answer:
is this correct? hope it works
Answer:
The difference of a number and 4 is 11
=> That number is 11 + 4 = 15
The quotient of a number and 13 is 78
=> The number is 13 x 78 = 1014
6.5 more than a number is 19.1
=> The number is 19.1 - 6.5 = 12.6
Hope this helps!
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Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
A builder makes drainpipes that drop 1 cm over a
horizontal distance of 30 cm to prevent clogs. See the
diagram below, which is not drawn to scale:
A certain drainpipe needs to cover a horizontal distance
of 700 cm
What is the length l of this drainpipe?
Round your answer to the nearest tenth of a centimeter
cm
Answer:
700.4 cm
Step-by-step explanation:
This involves two similar triangles.
Both triangles are right triangles.
One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.
(1 cm)^2 + (30 cm)^2 = c^2
c^2 = 901 cm^2
c = sqrt(901) cm
The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [sqrt(901) cm]/x
3/70 = sqrt(901) cm/x
3x = 70 * sqrt(901) cm
x = 70 * sqrt(901) cm/3
x = 700.4 cm
Answer: 700.4 cm
The length of drainpipe is 700.4 cm.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
One has legs measuring 1 cm and 30 cm.
Using Pythagorean theorem.
(1 cm)² + (30 cm)² = c²
c² = 901
c =√901 cm
Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [√(901) cm]/x
3/70 = √(901) cm/x
3x = 70 x √(901) cm
x = 700.4 cm
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Any help would be great
Which undefined term is used to define an angle?
O line
O plane
opoint
O ray
Answer:
A point would be used as the undefined term
The chances of a tax return being audited are about 21 in 1 comma 000 if an income is less than $100,000 and 29 in 1 comma 000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? Upper P (taxpayer with income less than $ 100 comma 000 is audited )equals nothing (Type an integer or a decimal.) What is the probability that a taxpayer with income of $100,000 or more will be audited? Upper P (taxpayer with income of $ 100 comma 000 or higher is audited )equals nothing (Type an integer or a decimal.) b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited?
Answer:
a) p=0.021
b) p=0.029
c) Exactly one audit: P=0.0965
More than one audit: P=0.0042
Step-by-step explanation:
a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:
[tex]p_1=\dfrac{21}{1,000}=0.021[/tex]
If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:
[tex]p_2=\dfrac{29}{1,000}=0.029[/tex]
b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:
[tex]P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\[/tex]
There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.
To calculate the probability that more than one will be audited, we use the same distribution:
[tex]P(x>1)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0) = \dbinom{5}{0} p^{0}q^{5}=1*1*0.8993=0.8993\\\\\\P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\\\P(x>1)=1-[P(x=0)+P(x=1)]\\\\P(x>1)=1-(0.8993+0.0965)\\\\P(x>1)=1-0.9958\\\\P(x>1)=0.0042[/tex]
There is a probability of 0.0042 that more than one out of a sample of five taxpayers with incomes under $100,000 will be audited.
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
Answer:
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
Step-by-step explanation:
The question is incomplete:
There is no data from the sample.
We will use the sample [105 107 117 106 110 ] as an example to solve the question.
The mean of the sample is:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(105+107+117+106+110)\\\\\\ M=\dfrac{545}{5}=109[/tex]
The standard deviation of the sample is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(105-(109))^2+(107-(109))^2+(117-(109))^2+(106-(109))^2+(110-(109))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(16)+(4)+(64)+(9)+(1)]}\\\\\\ s=\sqrt{\dfrac{94}{4}}=\sqrt{23.5}\\\\\\s=4.848[/tex]
This is a hypothesis test for the population mean.
The claim is that your team scored an average significantly less than 110 points.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.01.
The sample has a size n=5.
The sample mean is M=109.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.848.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.848}{\sqrt{5}}=2.17[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{109-110}{2.17}=\dfrac{-1}{2.17}=-0.46[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-0.46, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.46)=0.334[/tex]
As the P-value (0.334) 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 your team scored an average significantly less than 110 points.
A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout the year? Use the level of significance α= 0.05.
Birth Month Frequency
January-March 67
April-June 56
July-September 30
October-December 37
What are the null and alternative hypotheses?
Answer:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
Step-by-step explanation:
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference of birthdates distributed throughout the year
H1: There is a difference between birthdates distributed throughout the year
The level of significance assumed for this case is [tex]\alpha=0.05[/tex]
The statistic to check the hypothesis is given by:
[tex]\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The table given represent the observed values, we just need to calculate the expected values with the following formula [tex]E_i = \frac{total}{4}[/tex]
And replacing we got:
[tex]E_{1} =\frac{67+56+30+37}{4}=47.5[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
