the probability that an observation taken from a standard normal population will have a z value less than 0.5 and greater than ‒1.5, i.e., p(‒1.5
Answers
the probability that an observation taken from a standard normal distribution will have a z value less than 0.5 and greater than -1.5 is = 0.6247
To find the probability that a random observation from a standard normal distribution is between -1.5 and 0.5, we can use the standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table, we can find the area under the curve between -1.5 and 0.5. The table provides the cumulative probability for a standard normal distribution up to a certain z-score. Since we want to find the probability between -1.5 and 0.5, we need to subtract the area to the left of -1.5 from the area to the left of 0.5.
The area to the left of -1.5 is given by the cumulative probability for z = -1.5, which is 0.0668. The area to the left of 0.5 is given by the cumulative probability for z = 0.5, which is 0.6915.
Therefore, the probability that an observation taken from a standard normal distribution will have a z value less than 0.5 and greater than -1.5 is:
P(-1.5 < Z < 0.5) = P(Z < 0.5) - P(Z < -1.5) = 0.6915 - 0.0668 = 0.6247
So, the probability is approximately 0.6247
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Related Questions
Write in y= mx + b form: a line through (-3,1) having the same y-intercept as the graph of x-2y=-4
Answers
Step-by-step explanation:
Aight, so the same intercept
\( - 2y = - 4 - x = = = > \\ y = \frac{1}{2} x + 2\)
m=½
\(y = \frac{1}{2} x + b = = = > \\ now \: let \: us \: replace \: the \: point \\ 1 = \frac{1}{2} ( - 3) + b = = = > \\ \frac{5}{2} = b\)
soooo
\(y = \frac{1}{2} x + \frac{5}{2} \)
What should be subtracted from -1963 to obtain -9512
Answers
Step-by-step explanation:
no calculator at hand ?
-1963 - x = -9512
-x = -9512 + 1963 = -7549
x = 7549
so, 7549 has to be subtracted.
A geometric design. The design for a quilt piece is made up of 6 congruent parallelograms. What is the measure of ∠1?
f 120° g 30° h 150° j 60°
Answers
The angle measure of 1 is m∠1 = 60°.
Given information:
A geometric design. The design for a quilt piece is made up of 6 congruent parallelograms.
Let the angle measure of 1 is x.
As per the information provided, an equation can be rearranged as,
6x = 360
x = 360/6
x = 60.
Therefore, m∠1 = 60°.
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Adrian bought a car worth $12000 on 36 easy installments of $375. Answer the following questions. (1) How much total amount did Adrian pay in 36 months? Answer: Total payment A = $ (2) Identify the letters used in the simple interest formula I = Prt. I= $ P= $ and t years. (3) Find the rate of interest in percentage. Answer: r %. ASK YOUR TEACHER
Answers
3) since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.
(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:
Total payment A = Monthly installment * Number of installments
= $375 * 36
= $13,500
Therefore, Adrian paid a total of $13,500 over the course of 36 months.
(2) In the simple interest formula I = Prt, the letters used represent the following variables:
I: Interest (the amount of interest paid)
P: Principal (the initial amount, or in this case, the car worth)
r: Rate of interest (expressed as a decimal)
t: Time (in years)
(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:
r = (I / Pt) * 100
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line u - Line v, what is the value of x?
Answers
X=96/16
Solve
Solution
X=6
I WILL MARK BRAINLIEST PLEASE HELP
Answers
6=30
12=60
15=80
Step-by-step explanation:
for 6 mini she will use 30 pepperoni slices
if she uses 60 pepperoni slices =12 mini
for 16 mini she will use 80 pepperoni slices.
For confirmation use the graph table.
The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
Answers
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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Factorize the following expression ab-a-b+1
Answers
Group 'em together
a b − a + 1 − b
a b − a = a ( b − 1 )
Notice that there will be a 1 as without it it'll simply be ab
1 − b = 1 ( 1 − b )
Notice that it doesn't match with the upper one... so we'll change the signs
1 ( 1 − b ) = − 1 ( b− 1 )
(try to multiply them now!!
Jot them down in one expression
a ( b − 1 ) − 1 ( b − 1 )
You get!!!!!!
( a − 1 ) ( b − 1 )
Question 3 The point W(-13,9) was transformed to W'(-9, -13) by a rotation around the origin. Which of the following best describes this rotation? Answer 90° counterclockwise 270° counterclockwise 90° clockwise
Answers
The initial position of the point W (-13, 9)
The transformed position of the point W' (-9, -13)
when transformed 90 degrees counterclockwise, the coordinates of the original position is swapped and the y-coordinate is negated
That is if the W coordinate is (x,y), the transformation W coordinate in 90 degrees counter-clockwise will be (-y, -x )
Since W is (-13, 9)
Then W' will be ( -9 , -13)...In 90 degrees counterclockwise
the function f of x equals negative (x - 3 in the presidency squared plus sine can be used to represent the area of a rectangle with a perimeter of 12 units as a function of the length of the rectangle x what is the maximum area of the rectangle
Answers
Answer:
Step-by-step explanation:
Ft
what is the common factor of 1,50,000 and 50,000
Answers
Answer:
The common factor of 1,50,000 and 50,000 is 1
Hi!
I can help you with joy!
1,50,000 and 50,000 have lots of common factors.A factor is a number that a number is divisible by.Example: 2 is a factor of 10, because 10 is divisible by 2.Now, both of these numbers are divisible by1, 2, 5, 10, 20, 25, 50, 100, 1,000...Answer:
1, 2, 5, 10, 20, 25, 50, 100, 1,000...
Hope it helps.
Do comment if you have any query regarding my answer.
~Misty~
Find the perimeter of the figure. Round to the nearest tenth if
necessary.
Answers
Answer:
hfhufittitt748474uuttioe707po5i5tii5i4tio5
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞)
Answers
The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
What is value?Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.
This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).
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ABC is a company that manufactures screws for desk lamps. The design specification for the diameter of the screw is 0.8 ± 0.008 cm, where 0.8 is the "target" diameter and 0.008 is the tolerance.
1) After taking samples from the production line, the mean diameter is found to be 0.8 cm and the standard deviation is found to be 0.002 cm. Is the process 3-sigma capable? Is the process 6- sigma capable?
2) A year has passed and the ABC process mean is now 0.803 cm. Is the process 3-sigma capable? If not, how to improve the mean to make it 3-sigma capable (assuming standard deviation is fixed at 0.002), and how to improve the standard deviation to make it 3-sigma capable (assuming mean is fixed at 0.803)?
3) A year has passed and the ABC process mean is now 0.803 cm. Is the process 6-sigma capable? If not, how to improve the mean to make it 6-sigma capable (assuming standard deviation is fixed at 0.002), and how to improve the standard deviation to make it 6-sigma capable (assuming mean is fixed at 0.803)?
Answers
1) The process is 3-sigma capable but not 6-sigma capable because the process variation is smaller than the tolerance .
2) The process is not 3-sigma capable.
3) The process is not 6-sigma capable.
To determine whether the process is 3-sigma capable, we need to calculate the process capability index, also known as Cpk, which measures how well the process fits the design specifications.
Cpk is calculated as the minimum of two ratios: the ratio of the difference between the target value and the nearest specification limit to three times the standard deviation (Cpk = (USL - mean)/(3stdev) or (mean - LSL)/(3stdev)), and the ratio of the difference between the mean and the target value to three times the standard deviation (Cpk = (target - mean)/(3*stdev)).
For ABC's screw manufacturing process, the upper specification limit (USL) is 0.808 cm, and the lower specification limit (LSL) is 0.792 cm. With a mean of 0.8 cm and a standard deviation of 0.002 cm, the process capability index is:
Cpk = min((0.808 - 0.8)/(30.002), (0.8 - 0.792)/(30.002)) = 1.33
Since Cpk > 1, the process is 3-sigma capable. To determine if the process is 6-sigma capable, we need to calculate the process sigma level, which is the number of standard deviations between the mean and the nearest specification limit multiplied by two. The process sigma level can be calculated using the formula: Process Sigma = (USL - LSL)/(6*stdev).
For ABC's screw manufacturing process, the process sigma level is:
Process Sigma = (0.808 - 0.792)/(6*0.002) = 3.33
Since the process sigma level is greater than 6, the process is 6-sigma capable.
If the ABC process mean is now 0.803 cm, it is no longer 3-sigma capable since the mean is outside the target value range. To improve the mean to make it 3-sigma capable, ABC would need to adjust the production process to shift the mean towards the target value of 0.8 cm. This could involve changing the manufacturing process, adjusting the machinery, or modifying the materials used to manufacture the screws.
Assuming the standard deviation is fixed at 0.002 cm, we can calculate the new process capability index required to achieve 3-sigma capability. Using the formula for Cpk, we get:
Cpk = (0.8 - 0.803)/(3*0.002) = -0.5
To achieve 3-sigma capability, the process capability index needs to be greater than or equal to 1. Since -0.5 is less than 1, ABC would need to improve the mean diameter of the screws to make the process 3-sigma capable.
To improve the standard deviation to make the process 3-sigma capable, assuming the mean is fixed at 0.803 cm, ABC would need to reduce the amount of variation in the manufacturing process. This could involve improving the quality of the raw materials, enhancing the precision of the machinery, or adjusting the manufacturing process to reduce variability. If the standard deviation is reduced to 0.001 cm, the new process capability index would be:
Cpk = min((0.808 - 0.803)/(30.001), (0.803 - 0.792)/(30.001)) = 1.67
Since 1.67 is greater than 1, the process would be 3-sigma capable.
If the ABC process mean is now 0.803 cm, it is still 6-sigma capable since
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Evaluate. Then interpret the result in terms of the area above and/or below the x-axis. | (x3 - 2x) dx 2 [ = ] (x3 - 2x) dx = 1 (Type an integer or a simplified fraction.) 2
Answers
We evaluate the integral using the Fundamental theorem of Calculus, by using and antiderivative of the funtion in the integrand;
An antiderivative of x^3 - 2 x is = 1/4 x^4 - x^2
So we evaluate this antiderivative at the two limits of integration:
At x = 1 the antiderivative becomes: 1/4 (1) - 1 = - 3/4
At x = - 1/2 the antiderivative becomes: 1/4 (-1/2)^4 - (-1/2)^2 = - 15/64
Now we subtract the evaluation at the upper limit minus the evaluation at the lower limit:
- 3/4 - (-15/64) = - 33/64
Allow me to show you the actual area we have calculated in a graph for the integration:
The curve in blue is the original function you provided : f(x) = x^3 - 2x
You can see that there is an area above the x axis that has been integrated and that gives as a result a positive number.
The area below the x axis is the part of the integral that provides the negative part which as you see is dominant in this calculation, therefore resulting in a negative final result.
Please, make sure you type -33/64 in the box provided.
a magazine conducted a study on the calorie content in a number of different brands of hotdogs. the calorie content in 20 beef and 17 poultry hotdogs was recorded. they are interested in determining if there is a difference in mean calorie content between beef and poultry hotdogs, assume the normal distribution assumption holds. what is the appropriate hypothesis testing method?
Answers
The appropriate hypothesis testing method is the two-sample t-test for independent samples.
What is Two-sample t-test?
The two-sample t-test is a statistical hypothesis test that is used to compare the means of two independent samples, assuming that the population standard deviations are equal and the samples are normally distributed. The test is based on the t-distribution and is used to determine whether there is a significant difference between the means of the two samples.
The appropriate hypothesis testing method for this scenario is the two-sample t-test for independent samples. The null hypothesis would be that the mean calorie content of beef hotdogs is equal to the mean calorie content of poultry hotdogs. The alternative hypothesis would be that the mean calorie content of beef hotdogs is different from the mean calorie content of poultry hotdogs.
The two-sample t-test for independent samples would be appropriate in this case because we are comparing the means of two independent samples (beef hotdogs and poultry hotdogs) and the sample sizes are relatively small (less than 30) with an unknown population standard deviation. By assuming that the normal distribution assumption holds, we can use the t-distribution to determine the probability of observing the sample means if the null hypothesis is true.
The two-sample t-test can be performed using statistical software such as Excel, R, or Python. The test will output a t-value and a p-value, which can be used to make a decision about whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level (usually 0.05), then we would reject the null hypothesis and conclude that there is a significant difference in mean calorie content between beef and poultry hotdogs.
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Evaluate the indefinite integral. (use c for the constant of integration. ) int (3x - 2)**20 dx
Answers
The solution to the indefinite integral \(\int\limits {(3x-2)^{20}} \, dx\) is \(\frac{(3x-2)^{21}}{63} +C\).
Indefinite Integrals are the integrals that can be calculated by the reverse process of differentiation and are referred to as the antiderivatives of functions.
The process of finding the indefinite integral is called integration.
\(=\int\limits {(3x-2)^{20}} \, dx\\\\put \ 3x-2 = t\\\\3dx = dt\\\\=\frac{1}{3} \int\limits {(t)^{20}} \, dt\\\\=\frac{1}{63}t^{21} + C\)
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BF bisects ∠ABC, meaning that it divides it half. If m∠ABF = 39 , then determine m∠ABC.
Answers
Applying the definition of an angle bisector, the measure of angle ABC is calculated as: 78 degrees.
What is an Angle Bisector?An angle bisector divides an angle into two parts that are of equal angle measures.
Given that BF is the angle bisector of angle ABC, and the measure of one of the half angles is angle ABF = 39 degrees, then we have the following:
Measure of angle ABC = 2(measure of angle ABF)
Substitute
Measure of angle ABC = 2(39)
Measure of angle ABC = 78 degrees.
Therefore, applying the definition of an angle bisector, the measure of angle ABC is calculated as: 78 degrees.
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The Baltic Sea is almost completely surrounded by countries in Europe. The average depth of the Baltic Sea is 52 meters below the surface. The deepest point in the Baltic Sea is 407 meters lower than this. What is the deepest point in the Baltic Sea relative to the surface?
Answers
Answer:
The deepest point in the Baltic Sea relative to the surface is 459 meters.
Step-by-step explanation:
The average depth of the Baltic Sea is:
\( d_{1} = 52 m \)
The deepest point in the Baltic Sea is (lower than this):
\( d_{2} = 407 m \)
Hence, the deepest point in the Baltic Sea relative to the surface is given by:
\( d_{T} = d_{1} + d_{2} = 52 m + 407 m = 459 m \)
Therefore, the deepest point in the Baltic Sea relative to the surface is 459 meters.
I hope it helps you!
What would be the domain for {(-6, 4), (5, -1), (0, 3), (-2, 4)}
Answers
Answer:
-6, 5, 0, and -2
Step-by-step explanation:
The domain values are the x-values in a coordinate pair. Therefore, the domains would be -6, 5, 0, and -2.
I hope this helped you!
Five times a number is 16 less than thirteen times the same number. Find the number.
Answers
Answer:
2
Step-by-step explanation:
Let the number be \(x\). Writing an equation in terms of the number, \(x\), gives
\(5x=13x-16\).
Adding \(16\) to both sides gives
\(5x+16=13x\).
Then, subtracting \(5x\) from both sides gives
\(8x=16\),
and dividing by 8 on both sides simplifies to
\(x=2\).
Multiply 3y (2y + 8)
Обу? + 24y
обу + 24
Обу? + 24
обу + 24y
Answers
Answer:
\(6y {}^{2} + 24y\)
Step-by-step explanation:
For this- you use the rule of distribution
1. 3 x 2 = 6
y x y = y^2
6y^2
2. 3y x 8 = 24y
6y^2 + 24y
A car travels 87 miles north and
then 114 miles west.
What is the magnitude of the
car's resultant vector?
Hint: Draw a vector diagram.
[?] miles
Round your answer to the nearest tenth.
Answers
Answer:
143.4 miles
Step-by-step explanation:
To find the magnitude of the resultant vector, we have to use the Pythagorean theorem. The Pythagorean theorem is \(a^{2} +b^{2} =c^{2}\).
What is given: (Look at the attached photo)
a = 86 miles (north)
b = 114 miles (west)
c = ?
-
Now let us substitute and solve:
1) \(87^{2} + 114^{2} = c^{2}\)
2) \(7569 + 12996 = c^{2}\)
3) \(c^{2} =20565\)
4) \(c= \sqrt{20565}\)
5) \(c = 143.4\)
The magnitude of the car's resultant vector is approximately 143.4 miles, rounded to the nearest tenth.
Given that a car travels 87 miles north and then 114 miles west, we need to find the magnitude of the car's resultant vector.
To find the magnitude of the car's resultant vector, we can use the Pythagorean theorem since the car traveled north and west, forming a right-angled triangle.
Let's label the distance traveled north as "A" and the distance traveled west as "B."
Then the magnitude of the resultant vector "R" can be calculated using the formula:
R = √(A² + B²)
Given that the car travels 87 miles north (A = 87 miles) and 114 miles west (B = 114 miles), we can plug these values into the formula:
R = √(87² + 114²)
R = √(7569 + 12996)
R = √20565
R ≈ 143.4 miles
So, the magnitude of the car's resultant vector is approximately 143.4 miles, rounded to the nearest tenth.
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1.1 1.2 Completely simplify the expressions below: 1.1.1 -3(2x - 4y)² 1.1.2 x+2 3 5 x+1 Completely factorise the expressions below: 1.2.1 ny + 4z + 4y + nz 1.2.2 3x² - 27x+60
Answers
The factorized expressions is 3(x-4)(x-5).
We are given that;
The expression 3x² - 27x+60
Now,
1.1.1 After simplification
-3(2x - 4y)² = -12(x-y)²
1.1.2 x+2/3*5x+1
= (3x+5)/(3x+3)
1.2.1 ny + 4z + 4y + nz
= (n+4)(y+z)
1.2.2 3x² - 27x+60
= 3(x-4)(x-5)
Therefore, by the expression the answer will be 3(x-4)(x-5).
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Solve
x2 + x - 56 = 0
Answers
The answer would be 2x1=x so x would be 2
Step-by-step explanation:
Answer:
x = 7, - 8
Step-by-step explanation:
x^2 + x - 56 = 0
x^2 + 8x - 7x - 56 = 0
x ( x + 8 ) - 7 ( x + 8 ) = 0
( x - 7 ) ( x + 8 ) = 0
x - 7 = 0
x = 7
x + 8 = 0
x = - 8
See image attached for the question.
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
B, C
Step-by-step explanation:
that's the answerrr
Answer:
2/8 and 5/20 are Equivalent Fractions
B and C options are right ones
Use elementary row operations to transform the augmented coefficient matrix to echelon form. Then solve the system by back substitution. X₁-4x2 +5x3. = 23 2x₁ + x₂ + x3 = 10 -3x + 2x₂-3x3 = = -23 *** An echelon form for the augmented coefficient matrix is What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box(es) in your choice. OA. There is a unique solution, x₁ = x₂ = x3 - (Simplify your answers.) B. There are infinitely many solutions of the form x₁ = x2-x3-t where t is a real number. (Simplify your answers. Type expressions using t as the variable.) 21 OC. There are infinitely many solutions of the form x, .X₂S, X₁t where s and t are real numbers. (Simplify your answer. Type expression using s and t as the variables.) D. There is no solution.
Answers
The solution to the linear system is unique solution which is x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.
The correct answer is option A.
To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:
[1 -4 5 | 23]
[2 1 1 | 10]
[-3 2 -3 | -23]
We'll apply row operations to transform this matrix into echelon form:
1. Multiply Row 2 by -2 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[-3 2 -3 | -23]
2. Multiply Row 3 by 3 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[0 -10 6 | -68]
3. Multiply Row 2 by 10/9:
[1 -4 5 | 23]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
4. Multiply Row 2 by 4 and add it to Row 1:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
5. Multiply Row 2 by 10 and add it to Row 3:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 0 -4 | -34/3]
Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:
From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.
From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.
From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.
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1.70p−0.34q 0.17(q 1)−0.85(p−1) =0 =0 consider the system of equations above. how many (p, q)(p,q)left parenthesis, p, comma, q, right parenthesis solutions does this system have?
Answers
The system has exactly one solution, which is (p, q) = (-0.2118, -8.0).
We are given the system of equations:
1.7p - 0.34q = 0
0.17(q+1) - 0.85(p-1) = 0
We can simplify the second equation by distributing the 0.17 and 0.85 terms:
0.17q + 0.17 - 0.85p + 0.85 = 0
0.17q - 0.85p = -0.72
Now we have two equations in two variables, which we can solve using substitution or elimination. We will use elimination here.
Multiplying the first equation by 5, we get:
8.5p - 1.7q = 0
Multiplying the second equation by 2, we get:
0.34q - 1.7p = -1.44
Adding these two equations, we get:
6.8p = -1.44
p = -0.2118
Substituting this value of p into either of the original equations, we get:
1.7(-0.2118) - 0.34q = 0
q = -8.0
So the system has exactly one solution, which is (p, q) = (-0.2118, -8.0).
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find the slope and the y-intercept
Answers
Y intercept is (0,3)
an economist wondered if people who go grocery shopping on weekdays go more or less often on fridays than any other day. she figured that if it were truly random, 20% of these shoppers would go grocery shopping on fridays. she randomly sampled 75 consumers who go grocery shopping on weekdays and asked them on which day they shop most frequently. of those sampled, 24 indicated that they shop on fridays more often than other days. the economist conducts a one-proportion hypothesis test at the 1% significance level, to test whether the true proportion of weekday grocery shoppers who go most frequently on fridays is different from 20%. (a) which answer choice shows the correct null and alternative hypotheses for this test?
Answers
The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.
To solve this problem, we run a hypothesis test about the population proportion.
Proportion in the null hypothesis (p0) = 0.2
Sample size (n) = 75
Sample proportion (sp) = 24/75 = 0.32
Significance level = 0.01
\(H_{o}\) : p = 0.2
\(H_{a}\) : p ≠ 0.2
Test statistic percentage = ( \(sp\) - \(p_{o}\) ) / \(\sqrt{\frac{(p_{o})(1-p_{o} )}{n} }\)
Left critical \(z_{0.01}\) = -2.5758
Right critical \(z_{0.01}\) = 2.5758
Calculated statistic = \(\frac{0.32-0.2}{\sqrt{\frac{(0.32)(1-0.32)}{75} } }\) = 2.2278
Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.
Therefore,
The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.
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