Answer:
1)The sample mean is the point estimate for the starting salary of the graduates which is $32,000
2) at 95%, confidence interval for the average salary of all graduates is ( 31525.13, 32474.87 )
3) Margin of Error E = 474.87
4) at 99%, confidence interval is ( 31328.54, 32671.46 ).
5) the probability of error will be affected
Step-by-step explanation:
Given the data in the question;
1) the point estimate for the starting salary of the graduates?
The sample mean is the point estimate for the starting salary of the graduates which is $32,000
2) the 95% confidence interval for the average salary of all graduates?
given that;
mean x' = $32,000
standard deviation σ = $5000
sample size n = 300
∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05/2 = 0.025
Z Critical value [tex]Z_{\alpha /2[/tex] = 1.6449 ≈ 1.645
so, 95% confidence interval for the average salary of all graduates will be;
⇒ x' ± Margin of Error
Margin of E = [tex]Z_{\alpha /2[/tex] ( σ/√n )
we substitute
E = 1.645( 5000/√300 )
E = 1.645( 288.675 )
E = 474.87
so
x' ± Margin of Error
32000 ± 474.87
⇒ 32,000 - 474.87, 32,000 + 474.87
⇒ ( 31525.13, 32474.87 )
Therefore, 95% confidence interval for the average salary of all graduates is ( 31525.13, 32474.87 )
3) the value of the Maximum Tolerable Error for the above confidence interval?
This is simply the Margin of Error,
Margin of Error E = 474.87
4)
If the level of confidence changes to 99%, and all other variables remain unchanged, what will happen to the confidence interval?
at 99% confidence level;
∝ = 1 - 99% = 1 - 0.99 = 0.01
∝/2 = 0.005
[tex]Z_{\alpha /2[/tex] = 2.326
∴ confidence interval will be;
⇒ 32000 ± [tex]Z_{\alpha /2[/tex] ( σ/√n )
we substitute
⇒ 32000 ± 2.326( 5000/√300 )
⇒ 32000 ± 2.326( 288.675 )
⇒ 32000 ± 671.458
⇒ 32000 - 671.458, 32000 + 671.458
⇒ ( 31328.54, 32671.46 )
Therefore, at 99%, confidence interval is ( 31328.54, 32671.46 ).
5) If the number of graduates returning the survey changes from 300 to 700 and all other variables remaining unchanged, the probability of error will be affected
A dietitian is interested in the average amount of time teenagers exercise per week. Based on previous studies, teenagers exercise an average of 6.5 hours per week. The dietitian suspects this average has increased. During the process of hypothesis testing, the dietitian calculates a test statistic of 3.30. If this test statistic is higher than the critical value, what can the dietitian do next
Answer:
The dietitian should conclude that there is no significant evidence to support the claim that the number of hours teenagers exercise per week has increased.
Step-by-step explanation:
H0 : μ = 6.5
H1 : μ > 6.5
The test statistic value = 3.30
The critical value > test statistic
The Decison region :
If; test statistic > critical value (Fail to reject H0)
If; test statistic < Critical value (Reject H0)
Given that the test statistic is > critical value ; then we fail to reject the null
Hence, the dietitian should conclude that there is no significant evidence to support the claim that the number of hours teenagers exercise per week has increased.
solve the inequality
g/-100=6
Answer:
g = -600
Step-by-step explanation:
Is square root of 11 a irrational number
Answer:
yes I think square root of 11 is irrational no....
if 70kg is 20% of peter's weight, then what is peter's total weight!?
Cushing's disease is characterized by muscular weakness due to adrenal or pituitary dysfunction. To provide effective treatment, it is important to detect childhood Cushing's disease as early as possible. Age at onset of symptoms and age at diagnosis (months) for 15 children suffering from the disease were given in an article "Treatment of Cushing's Disease in Childhood and Adolescence by Transphenoidal Microadenomectomy" (New Engl. J. of Med., 1984: 889). Here are the values of the differences between age at onset of symptoms and age at diagnosis:
-24 -12 -55 -15 -30 -60 -14 -21
-48 -12 -25 -53 -61 -69 -80
Calculate a 95% confidence interval for the population mean difference, and interpret the resulting bound.
Answer:
Since the calculated value of t =-0.427 does not fall in the critical region so we accept H0 and conclude that there is enough evidence to show that mean difference in the age of onset of symptoms and age of diagnosis is 25 months .
Step-by-step explanation:
The given data is
Difference d= -24 -12 -55 -15 -30 -60 -14 -21 -48 -12 -25 -53 -61 -69 -80
∑ d= -579
∑d²= 29871
1) Let the hypotheses be
H0: ud= 25 against the claim Ha: ud ≠25
H0 : mean difference in the age of onset of symptoms and age of diagnosis is 25 months .
Ha: mean difference in the age of onset of symptoms and age of diagnosis is not 25 months.
2) The degrees of freedom = n-1= 15-1= 14
3) The significance level is 0.05
4) The test statistic is
t= d`/sd/√n
The critical region is ║t║≤ t (0.025,14) = ±2.145
d`= ∑di/n= -579/15= -38.6
Sd= 23.178 (using calculators)
Therefore
t= d`/ sd/√n
t= -38.6/ 23.178√15
t= -1.655/3.872= -0.427
5) Since the calculated value of t =-0.427 does not fall in the critical region so we accept H0 and conclude that there is enough evidence to show that mean difference in the age of onset of symptoms and age of diagnosis is 25 months .
Find the surface area of a basketball with a diameter of 10 in.
10 in
o 100T in
o 400T in
o 25T in?
o 10T in?
Answer:
100 pi in ^2
Step-by-step explanation:
The surface area of a sphere is
SA = 4 pi r^2
We need to find the radius
r = d/2 = 10/2 =5
SA = 4 * pi * (5)^2
= 4 * pi *25
= 100 pi in ^2
A regular ice cream cone is 5 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.75 inches.
(a)
Find the volume (in cubic inches) of the regular ice cream cone to the nearest tenth.
cu. in
(b)
Find the volume (in cubic inches) of the waffle cone to the nearest tenth.
cu. in
(c)
How much more ice cream (in cubic inches) fits in the waffle cone compared to the regular cone? Round your answer to the nearest tenth.
cu. in
Answer:
a 5
b49
c76
Step-by-step explanation:
Find the Volume.*
Of a 3x3 cube
Answer:
either 9 or 27
Step-by-step explanation:
most likely 27 because 3x3x3
Answer:
Cube number of 3 is 27
Step-by-step explanation:
cube of 3 is like 3×3×3 =27
A class’s test scores are normally distributed if the average score 60 and the standard deviation is 7 choose the spots where the students scoring below 46 and above 74 lie
Answer:
46
Step-by-step explanation:
We are given that a class's test scores are normally distributed with an average score of 60.
We know that the curve of a normal distribution is symmetric about its mean.
60-14=46
60+14=74
Hence, the point 46 lies to the left of the mean and 74 lies to the right of the mean, and the two points have the same function value.
Answer: Look at the picture below
Step-by-step explanation: I got this right on Edmentum
Rewrite the equation 8x + 6x^2 -7=x^2 in standard form and identify a, b, and c.
Answer:
[tex]5x^2+8x-7=0\\a=5\\b=8\\c=-7[/tex]
Step-by-step explanation:
The standard form of a quadratic is [tex]ax^2+bx+c=0[/tex]. You need to subtract the x^2 from the right to set the quadratic equal to 0. Then a,b, and c are equal to the values of the coefficients in front of the terms.
If this helped, a brainliest would be greatly appreciated!
How do you use a number line to find 3/4 times 2/5
Answer:
First, you need to find the number 2/5 on the number line.
Now, you want to find (3/4) times (2/5)
Then the distance between 0 and the point you found earlier needs to be divided into four equal parts (because the denominator is 4)
sAnd because we have the factor (3/4), with a numerator equal to 3, we move from the origin 3 of these parts to the right, the point at where you arrived is the point (3/4)*(2/5)
Another way, which should give you the exact same point, is:
First locate the point (3/4) on the number line.
Now, you want to find (3/4) times (2/5)
The distance between zero and the denominator needs to be divided into 5 parts (because the denominator is 5)
Because the numerator is 2, you need to move, from the origin, two of these parts to the right.
The point where you end is the product (3/4)*(2/5)
Is (1,8) a solution to the system of equations 3x+y=9 2x+9y=20
Which chocolate chip cookies have the greater spread in the number of chips per cookie?
is it
Regular
OR
Reduced Fat
Answer:
Reduced fat had the greater spread.
Step-by-step explanation:
I don’t Understand this who can help me
Step-by-step explanation:
The area of a square is
[tex] {s}^{2} [/tex]
where s is the side length.
It is given that the smaller square side length is s so that means the area of that smaller square is the formula above.
The longer square is twice the side length of the side length of the smaller square.
Since all squares have equal sides, that means all the side are twice than the smaller square sides.
We can represent that larger square area by
(4s) squared
To find how many smaller squares it would take to fill the larger square divide the formula by each other.
(4s)÷s squared =4
Solve this system of equations by substitution.
y = 4x
2x + y = 6
can someone please help me with this
Answer:
60 units^2
Step-by-step explanation:
area of triangle=base*height/2=8*15/2=120/2=60 units^2
Answer:
The answer would be 60 units ^2
Step-by-step explanation:
To find the area of a triangle, the formula is b x h (base times height) divided by 2. So in this case, the base would be 8 and the height would be 15. 8x15 = 120 divided by 2 (since it's a triangle) and the answer would be 60.
5. What is closest to the volume of the
sphere?
Answer:
The correct answer is D)
Step-by-step explanation:
To find the volume of a sphere, you need to use the formula [tex]\frac{4}{3}\pi r^3[/tex]. Since the radius of the sphere is 7.5 inches, you can use that to solve the volume. [tex]\frac{4}{3}\pi *7.5^3[/tex] = [tex]\frac{4}{3}\pi *421.875[/tex] = [tex]562.5*\pi[/tex] ≈ [tex]1767.15in^3[/tex], which is closest to [tex]1767.21in^3[/tex], so that is the correct answer.
Which would be the best method to use to solve the following equation. Explain your reasoning.
Methods:
Factoring
Square root Property
Completing the Square
Quadratic Formula
x^2-x-6=0
Method:
Why:
Answer:
x = 3 and x = -2
Step-by-step explanation:
The given equation is :
[tex]x^2-x-6=0[/tex]
We need to solve the given equation.
We can solve it using Completing the Square method.
We take two numbers such that their product is -6 and sum is -1.
So,
[tex]x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\x(x+2)-3(x+2)=0\\\\(x-3)(x+2)=0\\\\x=3\ and\ x=-2[/tex]
so, the values of x are 3 and -2.
Hi if you can help me that’d be great! Just show me the work/steps you took to answering the question and your explanation!
Answer:
x = 7
y = 16
upper 2 sides = 12
lower 2 sides = 19
Step-by-step explanation:
2x + 5 = x + 12
combine like terms:
x = 7
y - 4 = x + 5
y - 4 = 7 + 5
combine like terms:
y = 16
Upper sides = 7 + 5 = 12
Lower sides = 7 + 12 = 19
Kelly paid $45.36 for a sweater that was on sale for 25% off the original price. She paid 8% sales tax on the sale price.
What was the original price of the sweater, in dollars
The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.
Step-by-step explanation: Sorry if this doesn't help....
Please help ASAP.
There are 8 blue, 3, red, and 5 white straws in a cup. What is is the probability you reach and grab a white one for yourself and then a blue one for your friend?
the answer would be 2/16 or 1/8 :)
i will mark brainliest please help
A- less than -5
B- less than or equal to -5
C- Greater than -5
D- Greater than or equal to -5
I will mark you brainlist!
Answer:
C is the answer
Step-by-step explanation:
Determine any data values that are missing from the table, assuming that the data represent a linear function.
x y
1 2
2 4
3
a. 7
b. 6
c. 2
d. 8
Simplify the following rational expression.
(HELP PLS?)
Answer:
Simplified expression: [tex]\frac{1}{y+8 }[/tex].
The value of y that makes the expression undefined is y=-8.
Step-by-step explanation:
[tex]\frac{2y^{3}}{2y^{4}+16y^{3}}[/tex]
= [tex]\frac{2y^{3}}{2y^{3}(y+8) }[/tex]
(cancel out 2y³)
=[tex]\frac{1}{y+8 }[/tex]
A rational expression is undefined when the denominator (bottom number) is zero. So, if y equalled -8, the expression would ultimately equal [tex]\frac{1}{0}[/tex], which is undefined.
Jose reads his book at an average rate of 2.5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read 20 pages?
it would take him 32 minutes. You could use divisoin and multiplecation to figure it out
can someone help me with some of my math homework?
Answer:
H
Step-by-step explanation:
Answer:
H. -5x-50
Step-by-step explanation:
just distribution property
PLS HELP IlL GIVE BRAINLIEST
Find the area of the polygon. Complete the explanation to show how you found your answer.
7 cm 7 cm polygon 5 cm 9 cm
Add the area of the top rectangle, 7 ×
=
to the area of the bottom rectangle, 9 ×
=
. The area of the polygon is
?
sq cm.
As a group, students majoring in engineering disciplines have the highest salary expectations, followed by those studying the computer science fields, according to the results of a study. To compare the starting salaries of college graduates majoring in electrical engineering and computer science, random samples of 60 recent college graduates in each major were selected and the following information obtained.
Engineering Major: Mean 56202 and SD 2225
Computer Science Major: Mean 50657 and SD 2375
Required:
a. Find a point estimate for the difference in the average starting salaries of college students majoring in engineering and computer science. What is the margin of error for your estimate?
b. Based upon the results in part a, do you think that there is a significant difference in the average starting salaries for engineers and computer scientists? Explain.
Answer:
Sorry that's hard I don't n know the answer
Simplify (8 ÷ 24) ÷ 2
Answer:
1/6
Covert simplest
1/3÷2
1/6
