a) State the hypotheses in symbols:
H₀: p = 0.114 (null hypothesis: the county's proportion of vacant housing units is equal to the national proportion)
H₁: p ≠ 0.114 (alternative hypothesis: the county's proportion of vacant housing units is different from the national proportion)
b) Assumptions and conditions for 1-Proportion z-Test:
A. Randomization Condition
B. 10% Condition
D. Success/Failure Condition
E. Nearly Normal Condition
c) To perform a 1-Proportion z-Test, enter the following in your calculator:
1-PropZTest(0.114, 120/850, 850)
Test statistic (z): ≈ 2.24
P-value: ≈ 0.025
d) Sketch of the test distribution:
- Label the x-axis with the test statistic (z ≈ 2.24)
- For a two-tailed test, divide the p-value in half (0.025/2 = 0.0125) and label each half of the area under the curve
e) Conclusion:
Since the p-value (0.025) is less than the significance level (α = 0.05), we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of vacant housing units in the county is different from the national proportion of 11.4%.
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estimates its sales at 200,000 units in the first quarter and that sales will increase by 20,000 units each quarter over the year. they have, and desire, a 25% ending inventory of finished goods. each unit sells for $35. of the sales are for cash. 70% of the credit customers pay within the quarter. the remainder is received in the quarter following sale.
Based on the given information, the company estimates its sales to be 200,000 units in the first quarter. Assuming a 20,000 unit increase each quarter over the year, the second quarter's sales would be 220,000 units, the third quarter's sales would be 240,000 units, and the fourth quarter's sales would be 260,000 units.
To calculate the desired ending inventory of finished goods, we take 25% of the expected sales for the next quarter. For example, to determine the desired ending inventory for the first quarter, we take 25% of 220,000 units (the expected sales for the second quarter), which equals 55,000 units.
Each unit sells for $35, so the total sales revenue for the first quarter would be 200,000 units x $35 = $7,000,000.
Of the sales, 70% are for cash, so the company would receive $4,900,000 in cash for the first quarter's sales. The remaining 30% of sales are credit sales, and assuming that 70% of credit customers pay within the quarter, the company would receive an additional 21,000 units x $35 = $735,000 in the first quarter. The remainder of the credit sales, which is 30% x 30,000 units = 9,000 units, would be received in the following quarter.
Overall, the company expects to have increasing sales throughout the year and desires to maintain a 25% ending inventory of finished goods. The company also expects a mix of cash and credit sales, with 70% of credit customers paying within the quarter and the remainder paying in the following quarter.
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Find the measure of the missing angle. Round to the nearest degree.
The measure of the missing angle is38 degrees.
What is the measure of the missing angle?The figure in the image is a right triangle.
Missing angle θ = ?
Hypotenuse = 55
Opposite to angle θ = 34
To find the missing angle, we use the trigonometric ratio.
sine = opposite / hypotenuse
Plug in the given values and solve for the missing angle.
sinθ = 34/55
Take the sine inverse
θ = sin⁻¹( 34/55 )
θ = 38⁰
Therefore, the angle is 38 degrees.
Option A) 38⁰ is the correct answer.
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The cafeteria needs 800 onions. There are 20 onions in each bag. How many bags should the cafeteria buy?
The cafeteria should buy 40 bags of onions.
To find how many bags the cafeteria should buy, we need to divide the total number of onions needed by the number of onions in each bag:
Number of bags = Total number of onions / Number of onions in each bag
Substituting the given values, we get:
Number of bags = 800 onions / 20 onions per bag
Simplifying the expression on the right-hand side, we get:
Number of bags = 40 bags
The solution is a simple arithmetic calculation based on the formula for determining the number of bags needed to purchase, given the total number of onions necessary and the amount of onions in each bag. This approach includes dividing the total number of onions by the amount of onions in each bag to determine the number of bags needed.
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A random variable is a measurement to be taken in a probability experiment. an observed value of a random variable is the measurement that has been taken. a discrete random variable is a random variable in which there is a countable collection of possible observed values. that is:___________
The possible observed values of a discrete random variable can be listed in a countable collection. A random variable is a measurement to be taken in a probability experiment.
An observed value of a random variable is the measurement that has been taken. A discrete random variable is a random variable in which there is a countable collection of possible observed values. That is, the discrete random variable can only take on specific values within a given range, and the probability associated with each value can be calculated. This countable collection of possible observed values is finite or countably infinite, and the probabilities sum up to 1.
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You wish to test the following claim(Ha )at a significance level of α=0.05
H o :μ 1 =μ 2
H a :μ 1 <μ 2
You obtain a sample of size n1 =6 with a mean of x1 =72.9 and a standard deviation ofs 1=5.9 from the first population. You obtain a sample of size n 2=7
with a mean of xˉ =75.1
and a standard deviation of s 2=5.6
from the second population. Find a confidence interval for the difference of the population means. For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to three decimal places.) confidence interval
=
The test statistic is... the confidence interval contains zero all values in the confidence interval are below zero all values in the confidence interval are above zero This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean. The sample data support the claim that the first population mean is less than the second population mean. There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.
The pooled standard deviatio is 5.746. We can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.
First, we need to calculate the pooled standard deviation:
s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2))
s_p = sqrt(((6-1)*5.9^2 + (7-1)*5.6^2)/(6+7-2))
s_p = 5.746
Next, we can calculate the t-statistic:
t = ((x1 - x2) - 0) / (s_p * sqrt(1/n1 + 1/n2))
t = ((72.9 - 75.1) - 0) / (5.746 * sqrt(1/6 + 1/7))
t = -0.956
Using a t-distribution table with conservative degrees of freedom (df = min(n1-1, n2-1) = 5), we find that the critical value for a one-tailed test with α=0.05 is -1.833. Since our calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis.
Therefore, we cannot conclude that there is sufficient evidence to support the claim that the first population mean is less than the second population mean.
As for the confidence interval, we can use the formula:
(x1 - x2) ± t_(α/2, df) * s_p * sqrt(1/n1 + 1/n2)
Plugging in the values:
(72.9 - 75.1) ± t_(0.025, 5) * 5.746 * sqrt(1/6 + 1/7)
-4.019 < μ1 - μ2 < 0.719
Therefore, we can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.
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in the equation for the two-sample t test for independent samples, the difference between sample means is divided by a. The standard error of the mean b. standard error of the difference between means c. population standard deviation
d. sample standard deviation
In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.
The correct answer is b. The difference between sample means is divided by the standard error of the difference between means in the equation for the two-sample t-test for independent samples. This is because the standard error of the difference between means takes into account both sample sizes and sample variances, providing a more accurate estimate of the standard deviation of the difference between the two population means.
In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.
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Find the slope of a line perpendicular to the line whose equation is
3x−3y=63. Fully simplify your answer.
The slope of perpendicular line is -1.
We have,
Equation: 3x - 3y = 63
Now, writing the given equation in slope intercept form
3y= 3x- 63
y= 3x/ 3 - 63/3
y= x - 21
So, the slope of given equation is 1.
Now, the slope of two perpendicular line have the product -1.
let the slope of perpendicular line be m.
So, m x 1 = -1
m = -1
Thus, the slope of perpendicular line is -1.
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In how many ways can 8 distinguishable rooks be placed on an 8 × 8 chessboard so that none can capture any other, namely no row and no column contains more than one rook? For example, in a 2 × 2 chessboard, you can place 2 rooks labled 'a, and 'b' in 4 ways. There are 4 locations to place'a', and that location determines the location of b'. 40320 40320
In order to place 8 distinguishable rooks on an 8x8 chessboard without any of them being able to capture each other, you will need to ensure that each rook occupies a unique row and column.
Step 1: Place the first rook. There are 8 different locations to choose from (one in each row).
Step 2: Place the second rook. There are 7 remaining locations to choose from, as you cannot place it in the same row or column as the first rook.
Step 3: Place the third rook. There are 6 remaining locations to choose from, avoiding the rows and columns of the first two rooks.
Step 4: Continue this process until all 8 rooks have been placed.
To find the total number of ways to place the 8 distinguishable rooks, multiply the number of choices for each step:
8 (choices for rook 1) * 7 (choices for rook 2) * 6 (choices for rook 3) * 5 (choices for rook 4) * 4 (choices for rook 5) * 3 (choices for rook 6) * 2 (choices for rook 7) * 1 (choice for rook 8) = 40,320 ways.
To solve this problem, we can use the principle of multiplication. We start by placing the first rook in any of the 64 squares on the chessboard. There are 64 choices for the first rook.
Next, we need to place the second rook in a location that is not attacked by the first rook. Since rooks can attack any square in the same row or column as them, we need to choose a square that is not in the same row or column as the first rook. There are 7 rows and 7 columns remaining, so there are 14 squares in which the second rook can be placed.
For the third rook, we need to choose a location that is not attacked by either the first or second rook. This means we need to choose a square that is not in the same row or column as the first two rooks. There are 6 rows and 6 columns remaining, so there are 12 squares in which the third rook can be placed.
Continuing in this way, we see that the number of choices for the nth rook is equal to the number of rows and columns remaining after the (n-1)th rook has been placed. So, the total number of ways to place all 8 rooks on the chessboard is:
64 × 14 × 12 × 10 × 8 × 6 × 4 × 2 = 16,777,216
Therefore, there are 16,777,216 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.
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Pyramid A is a dilation with scale factor 4 of pyramid B. What is the volume of pyramid A in terms of the volume of pyramid B?
a) 0.25 times Va
b) 2 times Va
c) 8 times Va
d) 64 times Va
To get to her hotel, Nora has to take the correct exit on a roundabout that has a diameter of 22 yards. What is the roundabout's radius?
PLSSSS HELP IF YOU TRULY KNOW THISS
The answer resulted in x = 5 after the operation as the picture suggests, hope this helps
there are only red and blue cards in a box. the probability of choosing a red card in the box at random is one third. if there are 24 blue cards, how many cards are in a box?
There are 36 cards in the box. In this scenario, we are given that the probability of choosing a red card from a box is one-third. We also know that there are 24 blue cards in the box. Our goal is to find the total number of cards in the box.
Let's use the concept of probability to solve this problem. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability of choosing a red card is given as 1/3, and the favorable outcome is selecting a red card. Let R be the number of red cards, and T be the total number of cards in the box. The probability formula can be represented as:
Probability of choosing a red card = R / T
We are given that the probability of choosing a red card is 1/3:
1/3 = R / T
Since there are 24 blue cards in the box, we can represent the total number of cards as the sum of red and blue cards:
T = R + 24
Now, we can solve the system of equations to find the values of R and T:
1. 1/3 = R / T
2. T = R + 24
From equation 1, we can express R as:
R = (1/3) * T
Substitute this expression for R in equation 2:
T = (1/3) * T + 24
Multiplying both sides by 3 to eliminate the fraction, we get:
3T = T + 72
Subtracting T from both sides:
2T = 72
Now, divide by 2 to find the total number of cards, T:
T = 36
So, there are 36 cards in the box.
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Ready for More?
How can you show that a quadrilateral is a square with the fewest steps?
Answer:
Step-by-step explanation:
How can you show that a quadrilateral is a square with the fewest steps?all 4 sides equalall interior angles equal 90°
A semiconductor manufacturer produces controllers used in automobile engine applications. The customer required that the process fallout or fraction defective at a critical manufacturing step not exceed 0.05 and that the manufacturer demonstrate process capacity at this level of quality using α = 0.05. The semiconductor manufacturer takes a random sample of 200 devices and finds that four of them are defective. Can tha manufaturer demonstrate process capability for the customer?
if you wanted to test the hypothesis hop 0.06, h, p<0.06 you would reject the null hypothesis when this question is part of a quiz or exam at anzona state university, it may not be posted or reproduced without permission from the author and arizona state university answer not here of value a
The semiconductor manufacturer can demonstrate process capability for the customer, as the fraction of defective devices is less than 0.05 at the α = 0.05 significance level.
To answer your question, we will test the hypothesis with the given data. The hypothesis to be tested is:
H0: p = 0.05 (null hypothesis)
H1: p < 0.05 (alternative hypothesis)
Here, α = 0.05 (significance level), and the sample consists of 200 devices.
Step 1: Calculate the sample proportion of defective devices.
Sample proportion (p-hat) = (Number of defective devices) / (Sample size) = 4 / 200 = 0.02
Step 2: Calculate the test statistic (z-score).
z = (p-hat - p) / sqrt((p * (1 - p)) / n)
z = (0.02 - 0.05) / sqrt((0.05 * (1 - 0.05)) / 200) = -2.18
Step 3: Determine the critical z-score (z-critical) for the given α.
For α = 0.05 and a one-tailed test, the z-critical is -1.645.
Step 4: Compare the test statistic (z) with the critical z-score (z-critical).
Since z = -2.18 < z-critical = -1.645, we reject the null hypothesis (H0).
Conclusion: Based on the sample, the semiconductor manufacturer can demonstrate process capability for the customer, as the fraction of defective devices is less than 0.05 at the α = 0.05 significance level.
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Find x, and then any unknown angles in the quadrilateral.
X=
(Type a whole number)
M
The value of x in the quadrilateral is 20 degrees.
How to find the angles of a quadrilateral?The sum of angles in a quadrilateral is 360 degrees. Therefore, a quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angle.
Hence, let's find the value of x in the quadrilateral.
x + x + 32 + 8x - 16 + 8x - 16 = 360
2x + 16x + 32 - 32 = 360
18x + 0 = 360
18x = 360
18x = 360
divide both sides by 18
x = 360 / 18
x = 20
Therefore,
x = 20 degrees
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is (x + 1) a factor of x² + x³ + x + 1
Explanation please
10. Mrs. Johnson plans to cut a 6 foot (ft) board into pieces
3
that are ft long, as shown in the diagram below.
6 ft-
How many pieces can she get from this board?
A 9 pieces
B 8 pieces
6
pieces
D 4 pieces
M/J
4
There is 20 students in her class.
Here, we have,
3/10= size of slice;
we can get 3 slices from one pizza.
There are 6 pizzas..... 3x6=18;
there will be a remained of 1/10 from each pizza
because 3/10 is not an even number.
Now u would have (6) 1/10's.... So 1/10+1/10+1/10= 3/10 and 1/10+1/10+1/10=3/10.....
That makes two more slices for two more students......
18+2=20 slices for 20 kids in the class.
Hence, There is 20 students in her class.
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HELP FAST!!!
BEST ANSWER GETS BRAINLIEST
Explain why and how you got the answer too!!
Answer: D
Step-by-step explanation:
If something is to the power of it means multiply the fractions.
since all inside the parenthesis is being multiplied you can distribute that exponent
[tex](64h^{16} x^{4} )^{\frac{1}{2} }[/tex]
[tex]64^{\frac{1}{2} } h^{16(\frac{1}{2}) } x^{4(\frac{1}{2} )} }[/tex] reduce fraction in exponents
[tex]64^{\frac{1}{2} } h^{8 } x^{2} }[/tex] now for the 64^1/2 than means take the square root
[tex]8 h^{8 } x^{2} }[/tex] fractions are actually roots
Sorry x is k in question.#1Change from standard form to vertex formy= x²-8x+15
Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).
To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:
Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.
Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.
Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.
y = (x² - 8x + 16 - 16) + 15 // add and subtract 16
y = (x - 4)² - 1 + 15 // factor and simplify
Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.
y = (x - 4)² + 14
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2. A triangle has a side length of 2 inch and a side length of 3 inches. What could be the length, in inches, of the third side of the triangle? Complete the response grid in the Answer Document.
Answer
the third side can measure 2 in, 3 in, or 4 in
Explanation
inequality theorem
a + b > c
a + c > b
b + c > a
2 = a
b = 3
c = x
a + b > c
2 + 3 > x
5 > x
x= 4, 3, 2, or 1 in
a + c > b
2 + x > 3
x = 4, 3, or 2
b + c > a
3 + x > 2
x = 4, 3, or 2
Hector flips a fair coin, then rolls a standard number cube. What's the theoretical probability of flipping heads, then rolling a 1 or 2?
The probability of flipping heads, then rolling a 1 or 2 is
fraction form
The theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.
Now, We have;
The sample space for flipping a coin and rolling a number cube are:
Flipping a coin: {H, T}
There are 2 possible outcomes, since the coin is fair.
Rolling a number cube: {1, 2, 3, 4, 5, 6}
Since, There are 6 possible outcomes, since the number cube is standard
So, the total number of outcomes for the combined experiment is,
2 x 6 = 12.
The events of flipping heads and rolling a 1 or a 2 are independent,
Hence, The probability of flipping heads is,
⇒ 1/2,
And, The probability of rolling a 1 or 2 is,
⇒ 2/6,
So, the probability of flipping heads and rolling a 1 or 2 is;
= (1/2) x (2/6)
= 1/6
Therefore, the theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.
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The formula for the force between two objects is , where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for m.
The solution of the formula for the variable, m as required to be determined is; m = Fr² / GM.
What is the solution of the formula for variable m?It follows from the task content that the complete question indicates a formula;
F = GMm / r²
Hence, to solve for the variable m; multiply both sides by r² so that we have;
Fr² = GMm
Finally divide both sides by GM so that we have;
m = Fr² / GM
Ultimately, the formula with m as the subject is; m = Fr² / GM.
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Two more than the quotient of a number and 8 is equal to 4
The number that is two more than the quotient of a number and is equal to 4 is 16. Let's break down the sentence into a numerical condition:
"Two more than the remainder of a number and 8" can be spoken to as (x/8) + 2, where x is the number we are attempting to discover.
The sentence moreover states that this expression is "equal to 4", so we are able to type in
(x/8) + 2 = 4
To fathom for x, we will confine the variable on one side of the condition. We will start by subtracting 2 from both sides:
(x/8) = 4 - 2
Streamlining the right-hand side gives:
(x/8) = 2
At long last, we are able to illuminate for x by increasing both sides by 8:
x = 2 x 8
x = 16
thus, the number we are seeking out is 16.
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complete question: What is the number which is two more than the quotient of a number and 8 is equal to 4?
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translaion practice question
Answer:
4 units left
Step-by-step explanation:
Since you are changing the x value by negative 4, you move left towards the negatives 4 units.
The diameter of a circular cookie cake is 16 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.
100.48 square inches
200.96 square inches
401.92 square inches
803.84 square inches
There are 200.96 square inches that make up half of the cookie cake.
We have to given that;
The diameter of a circular cookie cake is 16 inches.
Now, We know that;
Area of circle = πr²
Here, Diameter = 16 inches
Hence, Radius = 16 / 2
= 8 in
Thus, Area of circular cookie cake is,
⇒ A = πr²
⇒ A = 3.14 × 8²
⇒ A = 200.96 inches²
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A square tile has a width of 1/4 foot how many tiles will fit end to end along a 4 food wall?
Answer:
16 tiles
Step-by-step explanation:
A teacher surveys 64 children on how they travelled to school. 20 of the students were in Year 7. The teacher surveyed 30% more students in Year 9 than in Year 7. The rest of the students surveyed were in Year 11. 75% of the students in Year 7 walked to school. 8 more students in Year 9 walked to school than did not walk. Out of students surveyed, more Year 11 students walked to school than Year 9 students. One of these students is picked at random Write down the probability that the student chosen will walk to school
The probability that the student chosen will walk to school is 0.5156.
Out of the 64 understudies (students) overviewed, let x be the number of understudies overviewed in Year 9.
At that point, we know that x = 1.3*20 = 26.
Out of the 20 understudies (students) studied in Year 7, 75% strolled to school, so 15 understudies in Year 7 strolled to school.
In Year 9, 8 more understudies strolled to a school than did not walk. Let w be the number of understudies in Year 9 who strolled to school.
At that point, the number of understudies in Year 9 who did not walk to school is x - w. So we have:
w + (x - w) = 26 (since x is the entire number of understudies overviewed in Year 9)
w - (x - w) = 8 (since 8 more understudies strolled to a school than did not walk)
Understanding this framework of conditions, we get w = 17 and x - w = 9
Out of the remaining understudies studied, which are in Year 11, we know that more strolled to a school than in Year 9.
In this manner, the likelihood that an understudy chosen at irregular strolls to school is:
P(walk to school) = (15 + 17 + x/4)/64
where x/4 is the number of understudies overviewed in Year 11 who strolled to school. We do not know the esteem of x/4, but we do know that it is more prominent than 9, since more understudies strolled to school in Year 11 than in Year 9.
In this manner, ready to say that:
P(walk to school) > (15 + 17 + 9)/64 = 0.5156
So the likelihood that a student chooses irregular walks to school is more noteworthy than 0.5156.
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Question 1 (True/False Worth 2 points)
(06.04 MC)
A student wrote the following resolution to a narrative about a day at the carnival.
As the sun began to set on the carnival, Livia couldn't help but feel a sense of accomplishment. It had been a day of fearful and fantastic firsts. Despite her fear of heights, she
had mustered up the courage to ride the Ferris wheel. As she walked around the booths and rides one last time she took in the sights and sounds. Then and there, she
promised herself not to let fear hold her back in the future. Now she was ready to take on whatever life threw her way.
P
The student says the resolution is effective because it ties up any remaining loose ends, shows how the characters have changed and what they have learned, and reveals a
universal theme.
This student's assessment of the resolution is correct.
O True
O False
The assessment that the student gave about resolution is correct hence the statement is true.
What is conflict resolution?A resolution is a decision that a person makes and it has to do with the will of the individual. As such the resolution has a lot to do with the ability of a person to be able to stand by the decision that he or she has been able to make as a result of careful thought.
In this case, the resolution neatly wraps up any unresolved issues, demonstrates the character's growth and lessons learned, and introduces a general theme.
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A food truck's revenue from the sale of Lacos and burritos is estimated to be R(t,b) dollars when t tacos and b burritos are sold. The following values are known. R(20.15) = 150 Rt,(20,15)= 3 Rb(20,15)=6 a. Estimate the food truck's revenue when 4 fewer burritos are sold. Selex b. How many tacos would the food truck need to sell to compensate for the decrease in burrito sales if the revenue is to remain at $150 Select
a. The new revenue can be estimated as R(20,11) = 150 - 24 = $126.
b. The food truck would need to sell 20 + 8 = 28 tacos to compensate for the decrease in burrito sales and keep the revenue at $150.
a. To estimate the food truck's revenue when 4 fewer burritos are sold, we can use the given information. We know that Rb(20,15) = 6, which means that the revenue changes by $6 for every additional burrito sold. If 4 fewer burritos are sold, the change in revenue would be 4 * (-6) = -$24.
b. To maintain a revenue of $150 despite selling 4 fewer burritos, we need to find out how many more tacos must be sold. We know that Rt(20,15) = 3, meaning the revenue changes by $3 for every additional taco sold. Since the loss in revenue due to selling 4 fewer burritos is $24, we need to sell enough tacos to make up for this loss. So, 24/3 = 8 more tacos need to be sold.
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Question 9 (1 point) A student at a university wants to determine if the proportion of students that use iPhones is different from 0.4. The hypotheses for this scenario are as follows. Null Hypothesis: p = 0.4, Alternative Hypothesis: p *0.4. If the student randomly samples 26 other students and finds that 9 of them use iPhones, what is the test statistic and p-value? 1) Test Statistic: 0.56, P-Value: 0.575 2) Test Statistic: -0.56, P-Value: 0.575 3) Test Statistic: -0.56, P-Value: 0.425 4) Test Statistic: -0.56, P-Value: 0.712 5) Test Statistic: -0.56, P-Value: 0.288
The probability of observing a test statistic as extreme or more extreme than -0.56, assuming the null hypothesis is true, is 0.575. The correct answer is 2) Test Statistic: -0.56, P-Value: 0.575.
The test statistic is calculated by taking the difference between the observed proportion (9/26 = 0.346) and the hypothesized proportion (0.4), and dividing by the standard error of the proportion. This gives a test statistic of -0.56.
The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated, assuming the null hypothesis is true. In this case, we are conducting a two-tailed test, since the alternative hypothesis is not specified as being greater than or less than 0.4. Using a standard normal distribution table or calculator, we can find the area under the curve that corresponds to a test statistic of -0.56, which is 0.575. This means that the probability of observing a test statistic as extreme or more extreme than -0.56, assuming the null hypothesis is true, is 0.575.
Therefore, the correct answer is 2) Test Statistic: -0.56, P-Value: 0.575.
In this scenario, the student is testing the null hypothesis (p = 0.4) against the alternative hypothesis (p ≠ 0.4) to determine if the proportion of students using iPhones is different from 0.4. The sample size is 26, with 9 students using iPhones. The test statistic is -0.56 and the p-value is 0.575. Therefore, the correct answer is option 2) Test Statistic: -0.56, P-Value: 0.575.
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