Answer:
The test statistics is [tex]z = -1[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The null hypothesis is [tex]H_o : \mu = \$30000[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 30000[/tex]
The sample mean is [tex]\= x = \$29,750[/tex]
The standard deviation is [tex]\sigma = \$2,500[/tex]
The level of significance is [tex]\alpha =0.05[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{29750 - 30000 }{ \frac{ 2500}{ \sqrt{100} } }[/tex]
=> [tex]z = -1[/tex]
From the desired test, we have that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 30000[/tex]The alternative hypothesis is: [tex]H_1: \mu < 30000[/tex]b) The t-statistic is t = -1.
Item a:
At the null hypothesis, we test if the average starting salary for clerical employees in the state is not less than $30,000, that is:
[tex]H_0: \mu \geq 30000[/tex]
At the alternative hypothesis, it is tested if the salary is less than $30,000, that is:
[tex]H_1: \mu < 30000[/tex]
Item b:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 29750, \mu = 30000, s = 2500, n = 100[/tex]
Hence, the t-statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{29750 - 30000}{\frac{2500}{\sqrt{100}}}[/tex]
[tex]t = -1[/tex]
The t-statistic is t = -1.
A similar problem is given at https://brainly.com/question/13873630
D
E
F
Using the Pythagorean Theorem, which of the following is true?
Answer:
D
Step-by-step explanation:
PLEASE HELP WILL MARK BEST!
Tristan and Devin are brother and sister. Their parents put a total of $200 a month into a
college account. Tristan just graduated from high school, and Devin has two years of high school left.
Suppose Tristan and Devin each graduate college 4 years after they graduate high school, and their
parents will continue to put $200 into the college account monthly until both children have graduated
from college. If there is $10,000 in the account right now, how much money should each child get per
year in order to get an equal share?
Answer:
I think the answer is 5,000 .
Find the smallest positive four-digit number that is divisible by each of the four smallest prime numbers.
Answer:
It might be 1,050. Also can't believe thats a college question-
It was very easy to solve! Help from an 8th grader here.
Step-by-step explanation:
The smallest four-digit number that is divisible by each of the four smallest prime numbers is 1050.
What is the divisibility rule?The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.
The four smallest prime numbers are 2, 3, 5, and 7.
To find the smallest four-digit number that is divisible by each of these numbers, we can start by finding the least common multiple (LCM) of these numbers. The LCM of a set of numbers is the smallest number that is divisible by all of the numbers in the set.
To find the LCM of 2, 3, 5, and 7, we can start by listing the prime factorization of each number:
2 = 2 x 1
3 = 3 x 1
5 = 5 x 1
7 = 7 x 1
Then, we can find the LCM by taking the highest power of each prime that appears in any of the numbers:
LCM(2, 3, 5, 7) = 2¹ x 3¹ x 5¹ x 7¹ = 210
Since we want the "smallest 4-digit number", then it is:
210 x 5 =1050
Therefore, each of the four lowest prime numbers may be divisible by the smallest four-digit number, which is 1050.
Learn more about the divisibility rule here:
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Using only the values given in the table for the function, f(x)=x^3-3x-2,
what is the interval of x-values over which the function is decreasing ?
Find the value of this expression if x = 5 and x=2
xy^2 / -3
Answer:
-20/3
Step-by-step explanation:
here x=5 and y=2 then put the value and get answer.
can u pls help with this question
Answer:
noooooooooooooooooooooooooooooooooooooooooooo
Step-by-step explanation:
In order to get a good workout on your treadmill, you figure you have to run 528 feet in one minute. What are the possible numbers of miles you have to run in 20 minutes to exceed this rate? (Hint: 1 mile = 5280 feet)
PLEASE PROVIDE AN EXPLANATION, thank you!
Answer:
2 miles.
Step-by-step explanation: Because 528 times 20 is 10560 then divide by 5280 equaling 2 miles.
Identify the graph that displays the speed of a car accelerating onto a highway until it reaches the speed limit, and then continuing on the highway at the speed limit.
Answer: D
Step-by-step explanation:
Graph D shows the car increasing speed over time, then, the flat line shows the car remains at a constant speed. In order for the scenario to apply, there needs to be a line parallel to the x-axis which shows a speed remaining the same over a given amount of time. D is the only graph which has this feature, thus this graph displays the scenario.
hellllllllllllllllp points if you answeer correctly
Answer:
the answer will be [-3/4,1/2]
Step-by-step explanation:
which pair of lines are perpendicular
Answer:
you're right!! its C
Step-by-step explanation:
For lines to be perpendicular, the multiplied slopes of the line need to be -1, so
y=1/3x-1
y=-3x-4
(1/3)*(-3)=-1
therefore, they are perpendicular
Charlie threw a ball up in the air modeled by the function f(x)=−x2+2x+4. Elizabeth release a balloon at the same time, represented by g(x)=2x. At what time do the paths cross and at what height?
Answer:
after 2 secsStep-by-step explanation:
The paths crossed at when the height are equal i.e when f(x) = g(x)
Given
f(x)=−x^2+2x+4
g(x) = 2x
IF f(x) = g(x), then;
−x^2+2x+4 = 2x
−x^2+2x+4 - 2x = 0
−x^2+4 = 0
-x^2 = -4
x^2 = 4
x = ±√4
x = 2 and -2
Time cannot be negative
Hence x = 2
The path crossed after 2 seconds
A line passes through the point (2,3) and has a slope of 0, what equation of the line?
A: y=2
B: y=3
C: x=2
D: x=3
Answer: B
Step-by-step explanation: put the points on a graph
Is this true or false ??
9.6x10^85/3x10^63 in scientific notation
Answer:
3.27*10^22
Step-by-step explanation:
Given the expression 9.6x10^85/3x10^63, we are to write it on scientific notation as shown:
9.6x10^85/3x10^63
= (9.8/3) * (10^85/10^63)
= (9.8/3) * 10^{85-63}
= (9.8/3) *10^22
= 3.27 *10^22
Hence the expression in scientific notation is 3.27*10^22
The cost of painting a wall that is 5 meters wide and 2 1/2 meters tall is $50. How many square meters can be painted for $1?
please answer asap
Answer: If the a and b of your formula mean how many hours it takes each
person, like a = 2 and b = 1, then the formula gives 3/2 or 1 hour and
30 minutes. This is not reasonable, since one of the painters alone
could do it in 1 hour.
Actually, your formula is UPSIDE DOWN. It should be (a*b)/(a+b).
Here's why.
Let h be the number of hours it takes for the two of them to do it
together. The first person could do it all in a hours, but can paint
only a fraction of the wall working h hours. Assuming a constant rate
of painting, that fraction is h/a. That is, the first painter will
paint h/a of the wall in h hours.
Similarly, the second painter will paint h/b of the wall in that time.
So, when will they be done? When the whole wall is painted, which
happens whenever those 2 fractions add up to 1.
You need to solve the following equation:
(h/a) + (h/b) = 1
h*b + h*a = a*b Multiplying through by a*b
h*(b+a) = a*b Factoring out h
h = (a*b)/(a+b) Dividing both sides by b+a
Okay, now say 3 painters could do it in a hours, b hours or c hours,
respectively. Let h be the number of hours they all must work to get
it all painted. The first painter finishes h/a of the wall in that
amount of time. The other 2 painters manage to paint h/b of the wall
and h/c of the wall in that time. Since h is the time to finish the
job, all 3 of these fractions must add up to the whole wall, or 1.
So you have the equation:
h h h
--- + --- + --- = 1
a b c
Solve this for h (start by multiplying through by a*b*c) and you will
get the generalized formula for 3 painters. It's not the formula you
wrote above but I think you can finish it off.
(I hope this helps. I'm sorry if it's wrong)
please explain steps
Answer:
122º
Step-by-step explanation:
The interior angles of a heptagon add to 900º. We can write an equation and solve:
(12x-9)º+(9x+14)º+(133)º+(10x+9)º+(10x)º+(136)º+(10x+5)º=900ºCombine like terms, 51xº+288º=900ºSubtract, 51xº=612ºDivide, xº=12ºNow that we know x, we can find the measure of ∠B:
∠B=9(12)+14=108+14=122ºA movie is being shown on television. The movie is scheduled for a 150 minute time lot and will include some commercial breaks. The number of commercial breaks can be determined by the equation 6x + 114 = 150, where x represents the number of commercial breaks.
A. Identify the meaning of the coefficient and the constant in the context of this situation.
B. Solve to find the number of commercial breaks.
C. Graph the solution.
Answer:
x=6
Step-by-step explanation:
5tgghjkli
What is the value
14x +18 = 118
Answer:
[tex]x = 7.142(appx)[/tex]
Step-by-step explanation:
[tex]14x + 18 = 118[/tex]
[tex] = > 14x = 118 - 18 = 100[/tex]
[tex] = > x = \frac{100}{14} = \frac{50}{7} = 7.142(appx)[/tex]
Does anyone know? How to do this?
Answer:
4 operations b/c thats how many is in the box
them you do addition using PEMDAS( perinthasis exponets multiplication division addition subtraction hope this is helpful
Step-by-step explanation:
The model y=1.8x−76.9 represents the relationship between the temperature (°F) and the number of ice cream cones sold. Using the model, approximate the temperature when there are 95 ice cream cones sold. Round your answer to the nearest tenth.
Answer: 75.1
Step-by-step explanation:
Answer:
86.0*
Step-by-step explanation:
i am not 100% sure
If the store paid $75 for a clarinet and sold it for $100, did the store mark up the price by 30%?
Answer:
No
Step-by-step explanation:
30% of $75 is $22.50 (0.3×75=22.5)
$75+$22.50=$97.50, not $100
So, the store did not mark up the price by 30% because the original price ($75) plus 30% more does not equal $100.
Answer:
no
Step-by-step explanation:
Use variables to write an equation that represents the relationships between the time x and the distance y.
An eagle flies 40 miles per hour.
An equation that represents the relationships is y = ?
An equation that represents the relationships between the time x and the distance y is y = 40x.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An eagle flies 40 miles per hour.
An equation that represents the relationships between the time x and the distance y:
Here, x and y are the variables.
So, the equation,
y = 40x.
Therefore, y = 40x is the required equation.
To learn more about the linear equation;
https://brainly.com/question/29739212
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Find the value
If a=4 b=7, and c=-5
3c
Answer:
=-15
Step-by-step explanation:
3c
3(-5)
3×-5
=-15
Here is a probability scale:
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
There are 3 white counters and 1 black counter in a bag.
I take one of the counters at random.
Put a cross on the probability scale to show the probability
that I have chosen the black counter.
Answer:
0.25
Step-by-step explanation:
3 white counters and 1 black counter,
3+1 = 4
the chances of you choosing the black counter is 1/4
1/4 can also be written as 0.25.
Answer:
The probability of choosing a black counter is 0.25.
Also the picture is attached for the mark on scale.
Step-by-step explanation:
Probability is the likeliness of occurrence of an event.
Given
There are three white and 1 black counter in the bag which means our sample space contains 3+1 = 4 elements
n(S) = 4
Let B be the event that the drawn out counter is black. As there is only one black counter
n(B) = 1
The probability of choosing a black counter is:
[tex]P(B) = \frac{n(B)}{n(S)}\\P(B) = \frac{1}{4} = 0.25[/tex]
Hence,
The probability of choosing a black counter is 0.25.
Also the picture is attached for the mark on scale.
There are 252525 students in Ms. Nguyen's second-grade class. In the class election, 444 students voted for Benjamin, 121212 voted for Sahil, and 999 voted for Maria.
Answer:
What is the question?? The question is not there
Answer:
129870 did not vote or voted for someone else.
Step-by-step explanation:
I don't know what your asking
Use mental math to solve the equation.
5) C-(-15) = 38
7) Write a pairs of negative intogoro
The diameter of a circle is 8 cm. What is the area of the circle? Use 3.14 for pi
Answer:
50.27
Step-by-step explanation:
convert 360m/s to km/h
Answer: 579.36 km/h miles to kilometers
1296 meters to kilometers
Step-by-step explanation: couldnt tell what you meant so both
Write the decimal equivalent for 6 1/9
Answer: 6.11
Step-by-step explanation:
Step 1: Multiply the whole number by the denominator:
6 × 9 = 54
Step 2: Add the product you got in Step 1 to the numerator:
54 + 1 = 55
Step 3: Divide the sum from Step 2 by the denominator:
55 ÷ 9 = 6.111111
That's it folks! The answer to 6 1/9 in decimal form is displayed below:
6 1/9 ≈ 6.11
Answer b.
Hope this answer helps you
Answer: b 6 1/9 = 6.11
Step-by-step explanation: what I did first was figure out the decimal version of 1.9 which equaled to 0.11111 etc. then due to it having a zero in front of it, you just place the in that spot making the answer 6.1111111 :)
hope this helped!
Independent random samples of released prisoners in the fraud and firearms offense categories yielded the given information on time served in months. At the 1% significance level, do the data provide sufficient evidence to conclude that the meantime served for fraud is less than that for firearms offenses? Assume that populations standard deviations are the same for both groups. (i.e., we assume σ1 = σ2 .)
Answer:
Since the computed value of t= -4.654 does not fall in the critical region we therefore accept the null hypothesis . We conclude that there is sufficient evidence to indicate a difference in the means time served for fraud is less than that for firearms offenses.
Step-by-step explanation:
Fraud Firearm
15.2 9.2 20.1 15.7
11.2 15.8 20.4 9.8
7.2 5.2 13.1 13.5
7.7 4.9 20.7 23.1
7.4 9.8 10.4 22.2
∑ 93.6 169
Fraud (X1i)² Firearm(X2j)²
231.04 84.64 404.01 246.49
125.44 249.64 416.16 96.04
51.84 27.04 171.61 182.25
59.29 24.01 428.49 533.61
54.76 96.04 108.16 492.84
∑1003.79 3079.66
We formulate the null and alternative hypothesis as
H0: μ1 - μ2 ≤ 0 i.e. the fraud meantime is less than that for firearms offenses.
Ha: μ1- μ2 > 0 i.e. the fraud meantime is greater than that for firearms offenses.
We set the significance level at ∝= 0.01
The test statistic, if H0 is true , is
t= x1`1- x`2/ Sp√1/n1+ 1/n2
which has a student t- distribution with ν= n1+ n2 -2 = 18 degrees of freedom
The critical region consists of all t- values which are greater than or equal to t> t(0.01)(18)= 2.522
Computations :
X1`= ∑X1i/n1 = 93.6/10= 9.36
X2`=∑X2j/n2=169/10 = 16.9
∑( X1i- x`1)² = ∑X1i²- (∑X1i)²/n1
= 1003.79 - 876.096/10
= 100.379- 87.6096
=12.7694
∑( X2j- x`2)² = ∑X2j²- (∑X2j)²/n2
= 3079.66 - 28561/10
= 3079.66- 2856.1
=223.56
Sp²= 12.7694+223.56/18= 13.129
Sp = √13.129 =3.623
t= 9.36-16.9/ 3.623√0.1+0.1
t= -7.54/ 1.62
t= -4.654
Conclusion: Since the computed value of t= -4.654 does not fall in the critical region we therefore accept the null hypothesis . We conclude that there is sufficient evidence to indicate a difference in the means time served for fraud is less than that for firearms offenses.
The meantime served for fraud is less than that for firearms offenses.