Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,463]. The population standard deviation used for the analysis is known to be $14,300.
a. What is the point estimate of the mean salary for all college graduates in this town?
Point estimate
b. Determine the sample size used for the analysis.
Sample size
Answers
Answer:
a. The point estimate was of $44,600.
b. The sample size was of 16.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
a. What is the point estimate of the mean salary for all college graduates in this town?
Mean of the bounds, so:
(38737+50463)/2 = 44600.
The point estimate was of $44,600.
b. Determine the sample size used for the analysis.
First we need to find the margin of error, so:
\(M = \frac{50463-38737}{2} = 5863\)
Relating the margin of error with the sample size:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.64.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
For this problem, we have that \(\sigma = 14300, M = 5863\). So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(5863 = 1.645\frac{14300}{\sqrt{n}}\)
\(5863\sqrt{n} = 1.645*14300\)
\(\sqrt{n} = \frac{1.645*14300}{5863}\)
\((\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2\)
\(n = 16\)
The sample size was of 16.
Related Questions
what is the equation of the offer?
a) y=8x -10
b) y=-6x + 5
c) y= - 0,8x + 45
d) y= + 0,8x+ 20
e) y= - 0,4x + 60
Answers
Answer:
D) y= + 0.8x + 46
Step-by-step explanation:
Hope it helps
Drag and drop a phrase to make the statement true.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
TrianglesABC and DEF are not similar triangles.
similar triangles
Two triangles, ABC and DEF. For triangle ABC, angle B is eighty degrees and angle C is sixty degrees. For triangle DEF, angle D is forty degrees and angle E is eighty degrees. PLS help with this im stuck
Answers
A phrase to make the statement true include the following:
Triangles ABC and DEF are similar triangles.
What are the properties of similar triangles?In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;
80° + 60° + m∠D = 180°
m∠D = 40°
Since angles D and E in triangle DEF are 80 degrees and 40 degrees respectively, we can logically deduce that both triangles ABC and DEF are similar.
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What is the product of the 4 x and the 3 x cubed y squared minus 2 x y cubed?
Answers
Answer:
4xy ×3xy -2xy
12xy-2xy
10xy
the are of the circle below is 28.26 ft. squared. What is the diameter
Answers
Answer: 8.06 Inches
The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.
At a toy story,Colton can buy a passage of 8 mini footballs for 10.40. The price per mini football is $ ?
Answers
Answer:
The 8-pack is a better value
Step-by-step explanation:
Mr Moore has 4 types of ice cream flavors. Each flavor can make 15 individual ice creams. 70% of these ice creams are in waffle cone. How many of these ice creams are in a waffle cone?
Answers
Answer:
42 ice creams in a waffle cone
Step-by-step explanation:
First we try to find how many ice cream does Mr. Moore has:
4*15=60 ice cream
It is said it 70% of these ice creams are in waffle cones. So 60*70/100= 60*7/10=6*7=42 ice creams in a waffle cone.
if all the solutions of the inequality x^2-6ax+5a^2
Answers
The number of possible integral values of 'a' is 4 and the possible value of a are 1, 2, 5, and 10.
here we have to find the number of possible integral values of 'a' that satisfy the given conditions, we need to compare the two inequalities:
x² - 6ax + 5a² <= 0
x² - 14x + 40 <= 0
Let's analyze each inequality separately:
x² - 6ax + 5a² <= 0
x² - 5ax -xa + 5a²<=0
(x - a)(x - 5a) <= 0
Case 1: (x - a) <= 0 and (x - 5a) <= 0
This implies a <= x <= 5a.
Case 2: (x - a) >= 0 and (x - 5a) >= 0
This implies x >= a and x >= 5a.
x² - 14x + 40 <= 0
x² - 10x-4x + 40 <= 0
(x - 4)(x - 10) <= 0
Case 3: (x - 4) <= 0 and (x - 10) <= 0
This implies 4 <= x <= 10.
Case 4: (x - 4) >= 0 and (x - 10) >= 0
This implies x >= 4 and x >= 10, which simplifies to x >= 10.
Case 1 (a <= x <= 5a) and Case 4 (x >= 10).
Since x >= 10, the lower bound of the intersection should be 10. We can substitute this value into the first inequality:
a <= 10 <= 5a
Dividing both sides by an (assuming a is positive), we get:
1 <= 10/a <= 5
To satisfy this condition, 'a' must be an integer divisor of 10. The integral values of 'a' that satisfy this condition are 1, 2, 5, and 10.
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Complete question:
if all the solutions of the inequality x² -6ax + 5a²<=0 are also the solutions of inequality x²- 14x + 40<=0 then find the number of possible integral values of a.
The question pertains to a quadratic inequality. A solution process could be carried out given the correct quadratic formula, although the initial inequality seems to contain a typo due to the lack of a comparison operator.
Explanation:The question you asked is about finding the solution to quadratic inequality x^2-6ax+5a^2. In general, the solutions or roots for any quadratic equation can be calculated using the formula: -b ± √b² - 4ac / 2a. Therefore, you can potentially apply this formula to your inequality.
However, it appears that there might be a typo in your question, as an inequality should have a comparison operator (like <, >, ≤, or ≥). If the full equation was x^2-6ax+5a^2 ≤ 0 or ≥ 0, we could carry out the solution process with the given formula.
I would recommend reviewing the question to ensure that it's written correctly. Once you have the correct inequality, you can apply the quadratic formula and solve for your variable 'x'.
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Which Zeros of the polynomial function partially graphed below have even multiplicity?
Answers
The Zeros of the polynomial function partially graphed below have even multiplicity are x = -3 and x = 3.
What are the Zeros of the Polynomial?
The zeros of a Polynomial graph are simply the points where the graph curve crosses the x-axis.
In simply terms, the Zeros of a function are the values of the independent variable that make the function equal to 0. Multiplicity just refers to how many copies of a given zero exist.
From the given graph, the zeros of the Polynomial function are x = 2 and x = 3 and x = -3
An odd multiplicity means the graph of the function crosses the x-axis at that point. An even multiplicity means the curve contacts the x-axis at that point and backs instead of crossing.
Thus, the odd multiplicity is at x = 3
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Pete has 4 packs of gum balls. Each pack has 5 gum balls. If Pete gives the same number of gumballs to 6 friends, how many gum balls will each friend get?
Answers
Answer:
3 gumballs with 2 left over
The measure of each interior angle of a regular polygon is 140", then number of sides that regular polygon has is ....................
Answers
The number of sides that the regular polygon has is 11.
The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0025. What is the probability that the diameter of a randomly selected pipe will exceed 0.9 inch?
Answers
Answer:
0.02275
Step-by-step explanation:
Standard deviation is the square root of variance
Standard deviation= Square(0.0025)= 0.05
Because of the normally distributed, the z- score for 0.9 inches is:
(0.9-0.8)/0.05= 2
-> P(x<= 0.9)= P(2) = 0.97725
-> P (x>= 0.9)= 1-0.97725 = 0.02275
Two students are solving the same problem: At a hardware store, they can cut a length of rope off of a big roll, so you can buy any length you like. The cost for 6 feet of rope is $7.50. How much would you pay for 50 feet of rope, at this rate?
-------------------------
a) Kiran knows he can solve the problem using a ratio table. What would be Kiran's answer?
Answers
Using ratio, the cost of 50 feet of rope costs $62.5
RatioThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. This can also be said to be a fraction of a quantity over another quantity.
In this question, the cost of 50 feet of the rope can be calculated using ratio.
This will be represented as
6 feet = $7.50
50 feet = x
Cross multiply both sides and solve for x
x = $62.5
The cost is $62.5
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The data below shows the money Paritosh spends on a weekend. What will be the central angles of each of these categories?with the numbers 40 100 50 50
Answers
The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:
Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.
Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).
Central angle for the first category: (40/240) * 360 = 60 degrees.
Central angle for the second category: (100/240) * 360 = 150 degrees.
Central angle for the third category: (50/240) * 360 = 75 degrees.
Central angle for the fourth category: (50/240) * 360 = 75 degrees.
The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.
These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.
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Note the search engine cannot find the complete question
si compro una camisa de 100 pesos con el 10% de descuento cuanto tengo que pagar en total
Answers
Answer:
$90
Step-by-step explanation:
10% de 100 es 10; 100-10=90
Answer:
90 pesos
Step-by-step explanation:
10% de 100 es 10. Resta esos 10 pesos de los 100, y te da tu resultado de 90 pesos.
Si necesitas que te lo explique mas, dime y te ayudare :)
Signature of the Principle investigator on the final proposal implies his responsibility for the following except
Answers
The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.
The signature of the Principal Investigator (PI) on the final proposal does not imply responsibility for certain aspects of the project beyond their control or expertise. While the PI plays a crucial role in leading and overseeing the research project, there are certain areas for which they may not bear direct responsibility.One aspect the PI may not be responsible for is the availability of funding. Although they may have been involved in securing the initial funding or writing the budget proposal, the final decision and availability of funds typically lie with funding agencies, institutions, or sponsors. The PI's signature on the proposal signifies their commitment to the project but does not guarantee funding.Additionally, the PI may not be accountable for the technical or scientific success of every aspect of the project. Research projects often involve interdisciplinary collaborations and multiple team members who contribute their expertise. The PI's signature signifies their leadership and overall responsibility, but they rely on the expertise and contributions of other team members for specific tasks and outcomes.Furthermore, the PI may not bear sole responsibility for external factors that can impact the project, such as changes in regulations, unforeseen events, or external market conditions. While they may adapt the project's direction and approach as needed, these external factors are beyond their direct control.In summary, the signature of the Principal Investigator on the final proposal does not imply responsibility for funding availability, technical success of every aspect, or external factors that may influence the project. The PI's role is primarily centered around leadership, coordination, and overall project management.The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?
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Advertising a business. Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.
Show all work
Answers
The inequality representing the given situation is -
300x + 700y ≤ 7500
What is advertising?Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.
Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.
We can write the inequality as -
300x + 700y ≤ 7500
where -
{x} - number of online ads posted
{y} - number of TV ads poste
Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.
Therefore, the inequality representing the given situation is -
300x + 700y ≤ 7500
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based on the data what is the difference between the median of the data including the outlier and excluding the outlier
Answers
The difference between the median is 0.5. option D
What is the difference?Getting the sets of values that we have in order, we can see that we have;
12, 15, 33, 45, 46, 51, 52, 93
We can find the median between 4th and 5th numbers this is now going to give us that; (45+46)/2 = 45.5
Median value = 45.5
We can see that 93 is the outlier in the data set so if we remove it we would have;
12, 15, 33, 45, 46, 51, 52
The median of the data set in this case is 45.
The difference is;
45.5 - 45 = 0.5
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Missing parts;
The number of lattes sold daily for two coffee shops is shown in the table:
Lattes
12
52
93
33
51
15
46
45
Based on the data, what is the difference between the median of the data, including the outlier and excluding the outlier?
A.46
B.45.5
C.45
D.0.5
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
Answers
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Given that ABCD is a rhombus, find the value of x. 4 (X +40) A. 75 B. 52 C. 25 D. 46 F. 26
Answers
the value of variable x in the rhombus is Option (c) 25.
Definition of a rhombusA parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.
Let O be the intersection point of the line AC and the line BD in the rhombus.
This two lines intersect at a 90° angle in the center. ( Property of Rhombus)
∠AOD=90°
According to the question:∠AOD+∠OAD+∠ODA=180° (triangle sum property)
90°+x+x+40°=180°
2x=180°-130°
x=25
Hence the value of x=25.
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find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
Answers
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6.7 % interest, bonds pay 2.5 % interest, and CDs pay 5.75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977.5 , how much was invested in each account?
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Answers
Answer:
stocks: $45000bonds: $55000CDs: $45000Step-by-step explanation:
You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.
SetupWe can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...
s + b + c = 145000b - c = 100000.067s +0.025b +0.0575c = 6977.50SolutionThese equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.
We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...
stocks: $45000bonds: $55000CDs: $45000__
Additional comment
Using b = c +10000, the two remaining equations are ...
s +2c = 1350000.067s +0.0825c = 6727.50<95141404393>
Two hens can lay 2 eggs in 2 minlutes if that is the maximum speed how many hens can lay 500 eggs in 500 minutes
Answers
To determine how many hens are needed to lay 500 eggs in 500 minutes, we divide 500 eggs by the number of eggs laid by each hen in 500 minutes. In this case, 500 eggs divided by 250 eggs per hen equals 2 hens.
So, you would need two hens to lay 500 eggs in 500 minutes at their maximum speed.
Mack is selling beaded necklaces and beaded wristbands at the Craft Market.
A necklace requires 40 minutes to make.
A wristband requires 25 minutes to make.
Mack has 360 minutes to make the necklaces and wristbands.
.
●
.
Additionally,
Mack wants to make no more than 12 items.
When Mack sells the necklaces and wristbands at the Craft Market, he will make $3.00 profit per necklace and
$2.00 profit per wristband.
Let x = the number of necklaces Mack makes.
.
.
Let y= the number of wristbands Mack makes.
TEXT ANSWER
Question 14
1 Points
Evaluate each vertex ordered pair in the profit function. Which vertex yields the maxi-
mum profit?
Answers
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
We have,
The profit function is given by:
P(x,y) = 3x + 2y
The constraints are:
40x + 25y ≤ 360 (time constraint)
x + y ≤ 12 (item constraint)
x, y ≥ 0 (non-negative constraint)
To find the vertices, we need to solve the system of equations for each pair of intersecting lines. The vertices are the points where the lines intersect.
40x + 25y = 360
x + y = 12
Solving this system of equations, we get:
x = 6, y = 6 (vertex 1)
x = 9, y = 3.6 (vertex 2)
x = 0, y = 12 (vertex 3)
Now, we evaluate each vertex in the profit function:
P(6,6) = 3(6) + 2(6) = 24
P(9,3.6) = 3(9) + 2(3.6) = 30.6
P(0,12) = 3(0) + 2(12) = 24
Now,
Vertex 2 yields a maximum profit of $30.60.
Therefore,
Mack should make 9 necklaces and 3.6 (rounded to 4) wristbands to maximize his profit.
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Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answers
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.
Suppose Charmaine borrows $7500 at an interest rate of 12% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.
Answers
AS per the concept of Compound interest,
(a), The amount owed at the end of 1 year is $8,400
(b) The amount owed at the end of 2 year is $ 9,408
Compound interest:
The general formula to calculate the compound interest is
A = P(1 + r/n)ⁿˣ
where
A represents Accrued amount (principal + interest)
P represents Principal amount
r represents Annual nominal interest rate as a decimal
n represents number of compounding periods per unit of time
x = time
Given,
Suppose Charmaine borrows $7500 at an interest rate of 12% compounded each year. Assume that no payments are made on the loan.
Here we need to find the following,
a)the amount owed at the end of 1 year.
b) the amount owed at the end of 2 year.
From the given details we know that the value of
Principal amount = $7,500
Interest rate = 12%
Part a) the amount owed at the end of 1 year is calculated as,
Here we have to convert R as a percent to r as a decimal
r = R/100
r = 12/100
r = 0.12 rate per year,
Then solve the equation for A
A = 7,500.00(1 + 0.12/1)(1)(1)
A = 7,500.00(1 + 0.12)(1)
A = $8,400.00
Therefore, the amount owed at the end of 1 year is $8,400.
Part b) The amount owed at the end of 2 year is calculated as,
In this one the value of principal amount interest rate are same but the value of year only differs as 2,
So, the amount is
=>A = 7,500.00(1 + 0.12/1)(1)(2)
=> A = 7,500.00(1 + 0.12)(2)
=> A = $9,408.00
Therefore, the amount owed at the end of 2 years is $9,408.
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Solve the equation.
x^2 − 4x + 4 = 3
Answers
sale of eggs that are contaminated with salmonella can cause food poisoning in consumers. a large egg producer takes an srs of 200 eggs from all the eggs shipped in one day. the laboratory reports that 9 of these eggs had salmonella contamination. unknown to the producer, 0.1% (one-tenth of 1%) of all eggs shipped had salmonella. identify the population, the parameter, the sample, and the statistic.
Answers
The simple random sample of 200 eggs
Statistic=Proportion of eggs in the sample that contain salmonella.
p = 0.045
The population is the individuals that are being studied.
population=All eggs in one day
A sample is the part of the population of which information was actually collected.
Sample=The simple random sample of 200 eggs
A parameter is a descriptive measure for a population.
Parameter=Proportion of eggs shipped that day that contain salmonella.
p = 0.1 % =0.001
A statistic is a descriptive measure for a sample.
STATISTIC=Proportion of eggs in the sample that contain salmonella.
p=9÷200 = 0.045
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For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
Answers
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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A normal distribution (X) has a mean of 100 and a standard deviation of 10.
What is the probability that X is between 90 and 110?
Answers
The probability that X is between 90 and 110 = 0.2 if a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.40.
What is a normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare. Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.
A normally distributed random variable x has a mean of 100
P(x < 90) = 0.4
The probability that X is between 90 and 110
Mean is 100
Hence P (< 100) = 0.5 as Mean is centered
Hence
P (90 < X < 100) = 0.5 - 0.4 = 0.1
The difference between 100 and 90 is 10
The difference between 100 and 110 is 10
and 100 is Mean
Hence P (100 < X < 110) = P (90 < X < 100) = 0.1
Adding Both
P ( 90 < X < 110) = 0.1 + 0.1 = 0.2
The probability that X is between 90 and 110 = 0.2
Using z score table.
Z = ( Value - Mean) /SD
Z score for 0.4 = -0.254
-0.253 = (90 - 100)/SD
SD ≈ 39.53
Z = ( 110 - 100)/39.53
Z = 0.253
For z score < 0.253, the probability is 0.6
Hence Probability in Between is 0.6 - 0.4 = 0.2
The probability that X is between 90 and 110 = 0.2
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