A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%;C, 40%;D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use α = 0.01.
Grade A B C D F
Number 36 42 60 14 8
a. 6.87
b. 0.6375
c. 5.25
d. 4.82
Answers
Answer:
\(E_{A} =0.25*160=40\)
\(E_{B} =0.25*160=40\)
\(E_{C} =0.4*160=64\)
\(E_{D} =0.05*160=8\)
\(E_{F} =0.05*160=8\)
And now we can calculate the statistic:
\(\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25\)
The answer would be:
c. 5.25
Step-by-step explanation:
The observed values are given by:
A: 36
B: 42
C: 60
D: 14
E: 8
Total =160
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference in the proportions for the final grades
H1: There is a difference in the proportions for the final grades
The level of significance assumed for this case is \(\alpha=0.01\)
The statistic to check the hypothesis is given by:
\(\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}\)
Now we just need to calculate the expected values with the following formula \(E_i = \% * total\)
And the calculations are given by:
\(E_{A} =0.25*160=40\)
\(E_{B} =0.25*160=40\)
\(E_{C} =0.4*160=64\)
\(E_{D} =0.05*160=8\)
\(E_{F} =0.05*160=8\)
And now we can calculate the statistic:
\(\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25\)
The answer would be:
c. 5.25
Now we can calculate the degrees of freedom for the statistic given by:
\(df=(categories-1)=(5-1)=4\)
And we can calculate the p value given by:
\(p_v = P(\chi^2_{4} >5.25)=0.263\)
The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis
Related Questions
Find the quotient below. Write the answer as a fraction in the simplest form 7 1/2 divided 5/6
Answers
Answer:
9
Step-by-step explanation:
steps for dividing mixed numbers.
Change every mixed number to an improper fraction.
Multiply the reciprocal of the divisor, simplifying if possible.
Put answer in lowest terms (or simpliest form)
Check to be sure the answer makes sense.
Raymond has a credit card with a 21.99% Apr. His balance this month is 3,000. Calculate how much interest he will pay this month. Round to the nearest cent.
Answers
The interest Raymond will pay this month is $54.98
What does APR mean?
APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate
monthly interest=21.99%/12
What is the monthly interest amount in dollars?
The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month
monthly interest=$3,000*21.99%/12
monthly interest=$54.98
Find out more about credit card balance on:https://brainly.com/question/6872962
#SPJ1
Which set of numbers has 11 as a common factor? {154, 231} {143, 221} {33, 39} {77, 91}
Answers
The set of numbers that have 11 as a common factor is {154, 231}.
What are common factors?The number that divides two or more numbers is called a common factor.
Given are the pair of numbers as -
{154, 231}
{143, 221}
{33, 39}
{77, 91}
The pair of numbers with the common factor 11 is {154, 231}.
Therefore, the set of numbers that have 11 as a common factor is {154, 231}.
To solve more questions on common factors, visit the link below -
https://brainly.com/question/11221202
#SPJ2
A metallurgist has one alloy containing 24% aluminum and another containing 60% aluminum. How many pounds of each alloy must he use to make 44 pounds of a third alloy containing 47% aluminum?
Answers
Answer:
15 8/9 pounds of 24%
28 1/9pounds of 60%
Step-by-step explanation:
x = pounds of 24%
44 - x = pounds of 60%
24x + 60(44 - x) = 47(44)
24x + 2640 - 60x = 2068
-36x + 2640 = 2068
-36x = -572
x = 15 8/9
44 - x = 28 1/9
Rounded
15 8/9 pounds of 24%
28 1/9pounds of 60%
six friends share 4 apples equally. How much apples does each friend friend get?
Answers
Cane buys candy in bulk and sells it at a 25% markup. If c represents the original cost of the candy, which expression represents the markup price?
Answers
Answer:
D
Step-by-step explanation:
A pre-election survey showed that two out of every three eligible voters would cast ballots in the county election. There are 390,000 eligible voters in the county. How many people are expected to vote in the election?
Answers
The number of people that nare expected to vote in the election is 260,000. people.
How to illustrate the fraction?Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.
In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.
The number of people expected to vote will be:
= Fraction of expected voters × Total number of people
= 2/3 × 390000
= 2 × 130000
= 260000
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
A sports news station wanted to know whether people who live in the North or the South are bigger sports fans. For its study, 175 randomly selected Southerners were surveyed and found to watch a mean of 3.8 hours of sports per week. In the North, 152 randomly selected people were surveyed and found to watch a mean of 4.8 hours of sports per week. Find a 95% confidence interval for the true difference between the mean numbers of hours of sports watched per week for the two regions if the South has a population standard deviation of 1.7 hours per week and the North has a population standard deviation of 1.2 hours per week. Let Population 1 be people who live in the South and Population 2 be people who live in the North. Round the endpoints of the interval to one decimal place, if necessary.
Answers
Using the z-distribution, it is found that the 95% confidence interval for the difference is (-1.3, -0.7).
What are the mean and the standard error for each sample?Considering the data given:
\(\mu_S = 3.8, n = 175, s_S = \frac{1.7}{\sqrt{175}} = 0.1285\)
\(\mu_N = 4.8, n = 152, s_N = \frac{1.2}{\sqrt{152}} = 0.0973\)
What is the mean and the standard error for the distribution of differences?The mean is the subtraction of the means, hence:
\(\overline{x} = \mu_S - \mu_N = 3.8 - 4.8 = -1\)
The standard error is the square root of the sum of the variances of each sample, hence:
\(s = \sqrt{s_S^2 + s_N^2} = \sqrt{0.1285^2 + 0.0973^2} = 0.1612\)
What is the confidence interval?It is given by:
\(\overline{x} \pm zs\)
We have a 95% confidence interval, hence the critical value is of z = 1.96.
Then, the bounds of the interval are given as follows:
\(\overline{x} - zs = -1 - 1.96(0.1612) = -1.3\)\(\overline{x} + zs = -1 + 1.96(0.1612) = -0.7\)More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Which of the following is the correct representation of permutation?
Answers
Answer:
Step-by-step explanation:
If is a permutation group of degree, then the permutation representation of is the linear representation of which maps to the corresponding permutation matrix (here is an arbitrary field). That is, acts on by permuting the standard basis vectors.
VI. In a class of 40 students, the marks obtained in Mathematics (out of 50) are as under: 44,50,44,49,42,47,45,42,44,48,49,48,47 49,47,41,45,48,41,48,41,42,47,49,49,48, 50.47.49.48.46.44.45.45.46.44.42.47.48.45 ow answer the following questions: a) b) c) d) e) Find the number of students getting more than 45 marks. Find the number of students getting less than 45 marks. Find the maximum number of students getting the same marks. Find the average marks obtained by the students in the class. Find the number of students getting more than average marks.
Answers
a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.
In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.
Counting these numbers, we find that there are 17 students who obtained more than 45 marks.
b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.
In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.
Counting these numbers, we find that there are 15 students who obtained less than 45 marks.
c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.
In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.
Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.
d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.
Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45
= 1912
Total number of students = 40
Average marks = Total marks / Total number of students
= 1912 / 40
= 47.8
Therefore, the average marks obtained by the students in the class is 47.8.
e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.
In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,
49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.
Counting these numbers, we find that there are 40 students who obtained more than the average marks.
In the multiplication shown, X, Y, Z are different non-zero digits. XYZ * 18 = ZXYY ; What is the three-digit number XYZ?
Answers
In the multiplication shown, X, Y, Z are different non-zero digits. XYZ * 18 = ZXYY ; Therefore, the solution is correct.
To solve this problem, we need to find the values of the three digits X, Y, and Z such that the multiplication of the three-digit number XYZ with 18 results in the four-digit number ZXYY.
Let's first write down the multiplication of XYZ with 18:
XYZ
x 18
-----
ZXYY
Since the last digit of the product is Y, we know that Z multiplied by 8 gives us a number ending in Y. This means that Z can be either 2 or 7. However, if we try Z=2, we can see that the product of XY2 with 18 would result in a three-digit number, which is not what we want. Therefore, we must have Z=7.
Now, let's perform the multiplication:
XYZ
x 18
-----
7YYZ
Since the product ends in Z, we know that X multiplied by 8 gives us a number ending in Z. This means that X can be either 1 or 6. However, if we try X=1, we can see that the product of 1YZ with 18 would result in a three-digit number, which is not what we want. Therefore, we must have X=6.
Now, we have:
6YZ
x 18
-----
7YYZ
Multiplying Y by 8 gives us a number ending in Z, which means that Y can be either 3 or 8. However, if we try Y=3, we can see that the product of 63Z with 18 would result in a four-digit number with a repeated digit, which is not what we want. Therefore, we must have Y=8.
Finally, we have:
68Z
x 18
-----
1232
By dividing both sides by 18, we get:
68Z 1232
÷ 18 = ---
------------
68
Simplifying this division, we get Z=4. Therefore, the three-digit number XYZ is 684.
To check our solution, we can perform the multiplication:
684
x 18
-----
12312
Therefore, the solution is correct.
To learn more about three-digit number visit;
https://brainly.com/question/12992284
#SPJ9
12. Determine the slope of the line having the equation 2x + y = 12
a. 2
b. -2
c. ½
d. -½
Answers
Answer:
b. -2
Step-by-step explanation:
Note the slope-intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
First, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides of the equation:
2x (-2x) + y = (-2x) + 12
y = -2x + 12
Remember, m is the variable for the term that stands for the slope (directly next to the x variable). In this case, your answer will be -2
b. -2 is your answer.
~
Answer:
b. -2
Step-by-step explanation:
2x+y=12
add -2x to both sides
y = -2x + 12
this is in slope intercept form y = mx + b
m meaning the slope
in this case the slope is -2
the answer will be b. -2
the question is 4 1/5 x 5/14
Answers
Answer:
3/2
Step-by-step explanation:
Simplify the following:
((4 + 1/5)×5)/14
((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:
((4 + 1/5)×5)/14
Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:
(((5×4)/5 + 1/5) 5)/14
5×4 = 20:
((20/5 + 1/5)×5)/14
20/5 + 1/5 = (20 + 1)/5:
(((20 + 1)/5)×5)/14
20 + 1 = 21:
(21/5×5)/14
21/5×5 = (21×5)/5:
((21×5)/5)/14
((21×5)/5)/14 = (21×5)/(5×14):
(21×5)/(5×14)
(21×5)/(5×14) = 5/5×21/14 = 21/14:
21/14
The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:
Answer: 3/2
14. Pick the corner point below that maximizes the following objective function: p=22x+14y (6,5)(0,0)(0,12)(15,0)(11,13)
Answers
Okay, here we have this:
Considering the provided function, we are going to replace the coordinate pairs one by one in the function, to observe which of the pairs maximizes the function, so we obtain the following:
(6, 5):
p=22x+14y
p=22(6)+14(5)
p=132+70
p=202
(0,0):
p=22x+14y
p=22(0)+14(0)
p=0+0
p=0
(0, 12):
p=22x+14y
p=22(0)+14(12)
p=0+168
p=168
(15, 0):
p=22x+14y
p=22(15)+14(0)
p=330+0
p=330
(11, 13):
p=22x+14y
p=22(11)+14(13)
p=242+182
p=424
Finally we obtain that the corner point that maximizes the function p=22x+14y is the last option (11, 13).
Steve's mom's age is 7 years less than 3 times Steve's ages.
Answers
Answer:
y = 3x + 7
(Not sure what the question was so, I just put it in slope intercept form)
Step-by-step explanation:
Let x be Steve's age.
Steve = x
Steve's Mom = y
Now let's create an equation:
y - 7 = 3x
y = 3x + 7
(Not sure what the question was so, I just put it in slope intercept form)
Please let me know if I misunderstood the question that way I can help you! <3
Answer:
Steve's mom is 65.
Step-by-step explanation:
Let s = Steve's age.
s + (3s - 7) = 65
4s - 7 = 65
4s = 72
s = 18
Check:
Steve is 18
His mom is (3 * 18) - 7 = 54 - 7 = 47
14 + 47 = 65
Yep.
18 + 47 = 65
Zane has 5 2/5 of soil for his garden. Each bag of soil will cover 20 square feet. How many square feet will zane be able to cover if he uses all these bags of soil?
Answers
5. Match the steps for constructing a congruent line segment to their pictures.
▼
▼
1. Step 2: Draw a second line
segment that is longer than the
first.
2. Step 4: That intersection is the
final endpoint of the copied
segment.
3. Step 1: Put the point of the
compass on one endpoint of the
segment to be copied. Change the
compass setting so that the
pencil end is just touching the
other endpoint, make a small arc
to see this.
4. Step 3: Without changing the
compass setting, put the
compass point on the new
endpoint on a new line. Make a
small arc that intersects the line.
Answers
We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:
Step 1 - Picture a
Step 2 - Picture b
Step 3 - Picture c
Step 4 - Picture c.
What is a line segment?Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.
The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.
A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.
Learn more about line segment on https://brainly.com/question/280216
#SPJ1
Answer:
Step-by-step explanation:
Determine the average rate of change of this function over the interval -2≤x≤4
Answers
The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.
A right prism has a triangle base. The length of the base is 12 yards and the height of the base is 3 yards. The height of the prism is 3.5 yards. What is the volume of the prism?
Answers
Answer:
c
Step-by-step explanation:
Question 2 of 15 Greece is different from most other countries in southern Europe because: A. its land has never been conquered by foreign empires. B. its most popular religion is not Catholicism. C. its culture has not spread to other regions. D. its population is mostly located in rural areas.
Answers
Greece is different from most other countries in southern Europe because its most popular religion is not Catholicism. Option B
What is Catholicism?Catholicism refers to the traditions, beliefs, and behaviors of the Catholic Church
Greece is predominantly an Orthodox Christian country, whereas most other countries in southern Europe, such as Italy, Spain, and Portugal, are predominantly Catholic.
Learn more about Catholicism at:https://brainly.com/question/929974
#SPJ1
Please answer this correctly
Answers
Answer:
18 roses
Step-by-step explanation:
In the given stem-leaf chart, 18 is the smallest number having 1 as "stem" and 8 as "leaf".
Identify the range of the function shown in the graph.
Answers
Answer:
Identify the range of the function shown in the graph.
Answer:
range=(10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10)
An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answers
Answer:
9
Step-by-step explanation:
The \(n\)term is \(2n+1\).
\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + \(n^2\) = 99
\(n^2\) + 2n - 99 = 0
Split the terms
\(n^2\) - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
Learn more about sum of n terms here
brainly.com/question/11688485
#SPJ1
What is the length of BD?
Answers
Answer:
D stays for 1 and as B is -6
the length of BD should be 7
good luck <3!
A law firm hires the same number of lawyers every year. At the end of 12 years, the firm has hired 48 lawyers. How many lawyers has the firm hired in the last 5 years?
Answers
Answer:
20 lawyers
Step-by-step explanation:
48 ÷ 12 = 4
which means every year 4 lawyers are hired
5 × 4 = 20
so this means the law firm has hired 20 lawyers in the last 5 years
Pls help this my last question!
Answers
Answer:
Step-by-step explanati
- |10+8l=-2
what is the simplified form of 4 log3x+6 log3y-7 log3z
Answers
Answer:
A
Step-by-step explanation:
Using the properties of logarithms, we can simplify the expression:
4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7
Now, we can use another property of logarithms, which states that:
loga (mn) = loga m + loga n
Using this property, we can combine the logarithms with addition or subtraction:
log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)
Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).
Un profesor de Enseñanza Básica le indica a sus alumnos que escojan tres dígitos
diferentes del conjunto {1, 2, 3, 4, 5} y formen números mixtos colocando los dígitos
en el casillero . También les recuerda que la parte fraccionaria tiene que ser
menor que 1, por ejemplo
2
3
5
. ¿Cuál es la diferencia entre el mayor y el menor de los
números mixtos que se pueden formar?
Answers
Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.
A mixed number is a number that has both a whole number and a fraction component. To form three-digit mixed numbers, we need to have a whole number that is less than 100 and a proper fraction that has a denominator less than or equal to 99. Here are some examples:123 4/567 2/8109 1/2382 3/47There are a total of 900 three-digit numbers that can be formed using digits 1 to 9 without repetition. To find the number of three-digit mixed numbers that can be formed, we need to count the number of ways we can choose a proper fraction with a denominator less than or equal to 99. There are 99 possible denominators, and for each denominator, there are 98 possible numerators (excluding 0 and the denominator itself). Therefore, the total number of three-digit mixed numbers that can be formed is:900 x 99 x 98 = 8,334,600There are 8,334,600 three-digit mixed numbers that can be formed using digits 1 to 9 without repetition.For such more question on fraction
https://brainly.com/question/78672
#SPJ8
The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.
How to solveThe three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.
The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.
The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.
The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.
Read more about algebra here:
https://brainly.com/question/4344214
#SPJ1
The Question in English
A Basic Education teacher tells his students to choose three digits
different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits
in the locker It also reminds them that the fractional part has to be
less than 1, for example
2
3
5
. What is the difference between the greatest and the least of the
mixed numbers that can be formed?
Write and solve an equation.
A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?
Answers
Answer:
13.25
Step-by-step explanation:
1. you have to subract the cost of the drink:
94.25-1.50=92.75
2.you have to divide to get the individual cost of pizzas by doing
92.75÷7=13.25
so therefore your answer is 13.25 per pizza
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30