According to researchers, a coin flip may not have a 50% chance of landing heads and a 50% chance of landing tails. In fact, they believe that a coin is more likely to land the same way it started. So if it starts out heads up, it is more likely to land heads up. Suppose someone tests this hypoth- esis with 1,000 flips of a coin where it starts out heads up each time. a. Describe what the symbol a stands for in this context. b. State your null and alternative hypotheses. c. Suppose 52% of the sample of 1,000 flips landed heads facing up. Verify the validity conditions that allow us to use a theory-based test. d. A theory-based test reports a standardized statistic of 1.26. Interpret what this means. e. A theory-based test reports a p-value of 0.1030. State your conclusion in terms of strength of evidence and what that means in the context of the study.
Answers
Answer:
a) π = np
π represents the number of heads that turn up in 1000 tosses of the coin.
b) The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
The validity conditions are met because we have 1000 tosses with 520 heads and 480 tails, indicating that we have more than 20 sample size in this sample.
The sample proportion (0.52) and the standard error of the sample proportion (0.0158) show that the distribution approximates a normal distribution and isn't skewed. So, the theory based test for this study is valid.
d) Check Explanation
e) The p-value obtained is greater than the significance level at which the test might have been performed, hence, we fail to reject the null hypothesis and conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
The researchers' claim then has to be wrong.
Step-by-step explanation:
a) If p corresponds to the proportion of 1000 tosses that turn up heads,
π = np
where n = number of tosses.
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question where we want to verify that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head. That is, the proportion of heads in multiple tosses is more than 0.5 given that the first toss was a head.
The null hypothesis would be that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
That is, the coin is likely to turn up heads less than or equal to 50% of the time, when it is tossed multiple times, starting with a first toss that gives a head.
The alternative hypothesis is that there is significant evidence to conclude that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Mathematically,
The null hypothesis is given as
The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The conditions that need to be satisfied before a theory based test is used include:
The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
d) The standardized statistic shows how far away from the standard proportion (the proportion that the population proportion is being compared with) the sample proportion is in terms of the standard error of the sample proportion.
It is given mathematically as,
t or z = (x - μ)/σₓ
x = p = sample proportion of the number of heads obtained in the multiple tosses starting with a first result of a head turning up = 0.52
μ = p₀ = 0.50 (the standard being tested against.
σₓ = standard error of the sample proportion, given as σₓ = √[p(1-p)/n]
n = sample size = 100
σₓ = 0.0158
The standardized statistic is also used to obtain the p-value that indicates how significant the results of the theory based test is.
e) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, like all other hypothesis testing, the significance level is usually at 0.05. On rare occasions, 0.01 and 0.10 are often used.
Whichever of the 3 is used,
p-value = 0.1030
0.1030 > 0.05, 0.01 or 0.10
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Hope this Helps!!!
Related Questions
This is for google classroom
Answers
The subject of this question is Science in Middle School. The student is learning about scientific models by making a model of air flow in their classroom or room in their house.
Explanation:The subject of this question is Science and the grade level is Middle School. In this question, the student is learning about scientific models by making a model of how air flows through their classroom or a room in their house. The student can use this activity to gain a better understanding of how air moves in closed spaces and the factors that affect its flow.
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The material for constructing the base of an open box costs 1.5 times as much per unit area as the material for constructing the sides. For a fixed amount of money C, find the dimensions of the box of largest volume that can be made.
Answers
The problem is an Optimization problem in Calculus that is solved by representing the volume of the open box in terms of a single variable using the fixed cost. With the volume equation, we can use calculus to find the optimal dimensions.
Explanation:The question is about maximizing the volume of an open box given a fixed cost and considering that the base of the box is 1.5 times as expensive as the sides. This problem comes under the branch of mathematics known as Optimization in Calculus. The volume V of an open box (a box without a top) is given by the product of its length, width, and height (V = lwh).
In this problem, the total cost is fixed, hence, the sum of the cost of the base and the cost of the sides is a constant. We can say that cost = C = (Base Cost) + (Sides Cost) = 1.5lw + 2.0lh + 2.0wh. We can express the width w in terms of l and h using the cost equation, and then substitute in the volume equation to write V in terms of a single variable. This enables the use of calculus to optimize the volume. It is beyond the scope of this answer to give a complete solution, but essentially, you would differentiate to obtain an equation, and solve for the optimal dimensions.
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which equations are equivalent to -1/4(x)+3/4=12 select all that apply
1.(-4x/1)+3/4=12
2.-1(x/4)+3/4=12
3.-x+3/4=12
4.1/4(x+3)=12
5.(-x/4)+3/4=12
Answers
Answer:
B C E are the answers
Step-by-step explanation:
hope it helps
Only the equations -1(x/4) + 3/4 = 12 and (-x/4) + 3/4 = 12 are equivalent to the original equation. The other equations provided do not hold the same properties of distribution and are not equivalent to the original equation.
Explanation:When comparing these equations to the original, we must take into consideration the properties of distribution, a crucial component of algebra. The original equation is -1/4(x) + 3/4 = 12. Let's go through the options one by one:
Equation 1: (-4x/1)+3/4=12. This one is not equivalent to the original equation because the coefficient of x in the original equation is -1/4, not -4.Equation 2: -1(x/4)+3/4=12. This equation is the same as the original one because -1/4 times x is the same as -1 times x/4.Equation 3: -x+3/4=12. This equation is not equivalent because the coefficient of x in the original equation is -1/4, not -1.Equation 4: 1/4(x+3)=12. This equation is not equivalent because the original equation does not have a term x+3 in it.Equation 5: (-x/4)+3/4=12. This equation is the same as the original one because dividing -x by 4 is the same as multiplying -1/4 times x.Learn more about Equivalent Equations here:https://brainly.com/question/34191741
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You wish to test the claim that mugreater than21 at a level of significance of alphaequals0.05 and are given sample statistics n equals 50 and x overbar equals 21.3. Assume the population standard deviation is 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal places.
Answers
Answer:
[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]
Step-by-step explanation:
Data given and notation
[tex]\bar X=21.3[/tex] represent the sample mean
[tex]\sigma=1.2[/tex] represent the population standard deviation
[tex]n=50[/tex] sample size represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 21, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 21[/tex]
Alternative hypothesis:[tex]\mu > 21[/tex]
If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z = \frac{21.3-21}{\frac{1.2}{\sqrt{50}}}= 1.77[/tex]
write 7.630 in word form.
Answers
Answer:
seven and six hundred thirty thousandths
Step-by-step explanation:
the decimal point is when you say and when reading it
The representation of 7.630 in word form is; Seven and six hundred thirty thousandths.
How to identify the place value of a digit in a number?The place values on left of decimal point start as ones, tens, hundreds, and so on.
The place value on right of decimal point starts from point and goes to right as tenths, hundreths and so on
The tens means multiply by 10
The tenth means tenth part of that digit which is that digit divided by 10
Place value of decimal numbers;
The given number is; 7.630
The given number can be written as;
7 and 0.630
Hence, the number can be pronounced as Seven and 630 thousandths.
However, we have,
Seven and six hundred thirty thousandths.
Hence, The representation of 7.630 in word form is; Seven and six hundred thirty thousandths.
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The net of a triangular pyramid. The base is D, and the sides are A, B, and C.
The net of the triangular pyramid shows the four faces of the pyramid labeled A, B, C, and D. Use the drop-down menus to complete the statements.
The base area is the total area of .
The lateral area is the total area of .
The surface area is the total area of .
Answers
Answer:
The base area is the total area of D
The lateral area is the total area of A, B, and C
The surface area is the total area of A, B, C, and D.
Answer:
(d) the base area is the total area
Explain: because i got it right on the test
Subtract 6 from me. Then multiply by 2. If you subtract 40 and then divide by 4 you get 8. What number am I?
Answers
Answer:
42
Step-by-step explanation:
work backwards And use the opposite operation
start with 8 x 4 = 32 + 40 = 72/2 = 36 + 6 = 42
Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 4%, and all stocks have independent firm-specific components with a standard deviation of 49%. Portfolios A and B are both well diversified. Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.6 2.4 39 B 2.3 -0.7 9
Answers
Answer:
E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)
Step-by-step explanation:
let us recall from the following statement:
The two independent economic factors are M1 and M2
Th risk free rate = 4%
The standard deviation of all stocks of independent firm specific components is =49%
P = portfolios for A and B
Now,
What is the expected relationship of return-beta
The Expected return-beta relationship E(rP) = % + βp₁ + βp₂
E(rA) = 4% + 1.6 * M1 + 2.4* M2 = 39%
E(rB) = 4% + 2.3 * M1 + (-0.7)* M2 = 9%
Therefore
Solving for M1 and M2 using excel solver, we have M1 = 5.50% and M2 = 10.92%
E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)
The question pertains to finance and investment analysis. It emphasizes the CAPM model, which combines systematic risk measured by beta and market risk premium to calculate expected returns on portfolios. It also highlights that diversification reduces firm-specific risks.
Explanation:The question deals with the concept of portfolio return, beta coefficients, and firm-specific risk, which are important aspects of finance and investment analysis. The expected return on portfolios A and B, can be calculated using the CAPM model, which states that expected return equals the risk-free rate plus the portfolio's beta (which measures systematic risk) multiplied by the market risk premium (difference between the expected market return and the risk-free rate). To compute this, the beta coefficients need to be multiplied with their respective economic factors, and the results obtained are added together.
For portfolio A, the expected return would be calculated like this: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (1.6 * M1) + (2.4 * M2).
For portfolio B, the calculation would be similar: Return = Risk-Free rate + β1*M1 + β2*M2 = 4 + (2.3 * M1) - (0.7 * M2). The negative beta on M2 indicates that the portfolio's return would decrease when M2 increases, hence it has an inverse relationship with the portfolio return. The independent firm-specific component would not affect the return as per the assumption that the portfolios are well diversified; diversification reduces, but not completely eliminates, the firm-specific risk.
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Find the quotient of 2/5 and 4/5
Give your answer as a fraction in its simplest form.
Answers
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
What is the quotient?
The quotient is the number which is generated when we perform division operations on two numbers.
The quotient of 2/5 and 4/5.
The quotient of 2/5 and 4/5 is determined in the following steps given below.
[tex]\rm Quotient =\dfrac{\dfrac{2}{5}}{\dfrac{4}{5}}\\\\Quotient =\dfrac{2}{5}\times \dfrac{5}{4}\\\\ Quotient =\dfrac{2}{4}\\\\Quotient =\dfrac{1}{2}[/tex]
Hence, the quotient of 2/5 and 4/5 is 1/2.
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Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five students who recently took the exam are 570, 620, 710, 540 and 480. We want to find a 95% confidence interval of the population mean of SAT math scores. Calculate the point estimate.
Answers
Answer:
The mean calculated for this case is [tex]\bar X=584[/tex]
And the 95% confidence interval is given by:
[tex]584-2.776\frac{86.776}{\sqrt{5}}=476.271[/tex]
[tex]584+2.776\frac{86.776}{\sqrt{5}}=691.729[/tex]
So on this case the 95% confidence interval would be given by (476.271;691.729)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=584[/tex]
The sample deviation calculated [tex]s=86.776[/tex]
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=5-1=4[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that [tex]t_{\alpha/2}=2.776[/tex]
Now we have everything in order to replace into formula (1):
[tex]584-2.776\frac{86.776}{\sqrt{5}}=476.271[/tex]
[tex]584+2.776\frac{86.776}{\sqrt{5}}=691.729[/tex]
So on this case the 95% confidence interval would be given by (476.271;691.729)
Final answer:
The point estimate of the population mean of SAT math scores, calculated from the sample scores (570, 620, 710, 540, and 480), is 584.
Explanation:
The subject of this question is Mathematics, specifically focusing on statistics and the SAT examination scores. To calculate the point estimate for the given simple random sample of SAT Mathematics test scores (570, 620, 710, 540, and 480), we need to find the sample mean. This can be done by adding all the scores together and dividing by the number of students in the sample, which is five in this case.
Point Estimate calculation:
Add all the scores together: 570 + 620 + 710 + 540 + 480 = 2920
Divide by the number of students: 2920 / 5 = 584
The point estimate of the population mean of SAT math scores is 584.
The mean time required to repair breakdowns of a certain copying machine is 93 minutes. The company which manufactures the machines claims that breakdowns of its new, improved model are easier to fix. To test this claim, sample of 73 breakdowns of the new model were observed, resulting in a mean repair time of 88.8 minutes and a standard deviation of 26.6 minutes. Use significance level α = 0.05. State clearly what are your null and alternative hypothesis, show your work, and state your conclusion.
Answers
Answer:
[tex]t=\frac{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349[/tex]
[tex]p_v =P(t_{(72)}<-1.349)=0.0908[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=88.8[/tex] represent the sample mean
[tex]s=26.6[/tex] represent the sample standard deviation for the sample
[tex]n=73[/tex] sample size
[tex]\mu_o =93[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean i lower than 93 min, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 93[/tex]
Alternative hypothesis:[tex]\mu < 93[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{88.8-93}{\frac{26.6}{\sqrt{73}}}=-1.349[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=73-1=72[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(72)}<-1.349)=0.0908[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can't concluce that the true mean is less than 93 min at 5% of signficance.
The null hypothesis is that the mean repair time for the new model is equal to the mean repair time for the previous model. The alternative hypothesis is that the mean repair time for the new model is less than the mean repair time for the previous model. By performing a one-sample t-test, we compare the sample mean repair time to the population mean repair time. Using the calculated t-statistic and the critical t-value, we determine whether to reject or fail to reject the null hypothesis.
Explanation:The null hypothesis, denoted as H0, states that the mean repair time for the new model of copying machine is equal to the mean repair time for the previous model (93 minutes). The alternative hypothesis, denoted as H1, states that the mean repair time for the new model is less than 93 minutes.
To test these hypotheses, we can perform a one-sample t-test. Using the given sample data, we calculate the t-statistic as:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Using the t-distribution table or a calculator, we find the critical t-value at a significance level of 0.05 and degrees of freedom (sample size - 1). If the calculated t-statistic is less than the critical t-value, we reject the null hypothesis and conclude that the new model has a lower mean repair time. Otherwise, we fail to reject the null hypothesis.
In this case, the calculated t-statistic is:
t = (88.8 - 93) / (26.6 / sqrt(73)) ≈ -1.34
With 72 degrees of freedom, the critical t-value at α = 0.05 is -1.666. Since the calculated t-statistic (-1.34) is greater than the critical t-value (-1.666), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the new model of copying machine has a significantly lower mean repair time than the previous model.
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what is y?
2y + 3 = 19
Answers
Answer:
y = 8
Step-by-step explanation:
2y + 3 = 19
2y = 19 - 3
2y = 16
y = 16/2
y = 8
Hopefully this help u
Answer: y = 8
Step-by-step explanation: To solve for y, we must first isolate the term containing y which in this problem is 2y.
Since 3 is being added to 2y, we subtract 3 from
both sides of the equation to isolate the 2y.
On the left, the +3 and -3 cancel
out and on the right, 19 - 3 is 16.
So we have 2y = 16.
Now we can finish things off by just dividing
both sides of the equation by 2.
On the left the 2's cancel and on
the right, 16 divided by 2 is 8.
So y = 8.
What does (-3/4)(-4/7)(-2/3 equal to please show work!?
Answers
Answer:
-2/7 0r 2/-7 or the negative sign is in the middle
Step-by-step explanation:
(-3/4)(-4/7)= 3/7
3/7 x -2/3= -2/7
What is the midpoint of EC ?
A: (t + p, r)
B: (p – t, r)
C: (p, r)
Answers
Given:
Given that the graph OACE.
The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)
We need to determine the midpoint of EC.
Midpoint of EC:
The midpoint of EC can be determined using the formula,
[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
Substituting the coordinates E(2t,0) and C(2p, 2r), we get;
[tex]Midpoint=(\frac{2t+2p}{2},\frac{0+2r}{2})[/tex]
Simplifying, we get;
[tex]Midpoint=(\frac{2(t+p)}{2},\frac{2r}{2})[/tex]
Dividing, we get;
[tex]Midpoint=(t+p,r)[/tex]
Thus, the midpoint of EC is (t + p, r)
Hence, Option A is the correct answer.
1,050,200
What is the number between 1 and 10
Answers
23 × 52 × 59 × 89
(2 × 2 × 2 × 5 × 5 × 59 × 89)
What is the solution to the following system?
3x+10y-12z=40
x-5y=0
x-4z=0
Answers
9514 1404 393
Answer:
(x, y, z) = (20, 4, 5)
Step-by-step explanation:
The last two equations allow y and z to be expressed in terms of x, so we have ...
3x +2(5y) -3(4z) = 40
3x +2(x) -3(x) = 40
x = 20 . . . . . . . . . . . . divide by the coefficient of x
y = 20/5 = 4
z = 20/4 = 5
The solution is (x, y, z) = (20, 4, 5).
You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provide housing for most of these women. After recording data for a whole year, you find that the mean number of women in shelters each night is 250, with a standard deviation of 75. Fortunately, the distribution of the number of women in the shelters each night is normal, so you can answer the following question posed by the city council.
If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights? If not, what number of shelter openings will be needed?
Answers
Answer:
Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.
274 shelters will be needed.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 250, \sigma = 75[/tex]
If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?
What is the percentile of 350?
This is the pvalue of Z when X = 350.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 150}{75}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a pvalue of 0.9082.
Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.
If not, what number of shelter openings will be needed?
The 95th percentile, which is X when Z = 1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 150}{75}[/tex]
[tex]X - 150 = 1.645*75[/tex]
[tex]X = 274[/tex]
274 shelters will be needed.
The current shelter capacity of 350 will not be sufficient for 95% of nights according to the normal distribution of the number of women in shelters each night. To have enough capacity for 95% of the nights, the city's shelter would need approximately 397 bed openings.
Explanation:The subject of this question relates to a discipline in statistics called normal distribution. Essentially, we have the mean number of women in shelters each night (250) and the standard deviation (75). Since the council wants the capacity to be enough for 95% of nights, we need to find the number corresponding to the 95th percentile in this normal distribution.
In a normal distribution, 95% of the data falls within 1.96 standard deviations of the mean. So, we will calculate the upper limit of the capacity using the following formula: Upper Limit = Mean + (1.96 * Standard Deviation)
By substituting the given mean and standard deviation (250 and 75 respectively), we get: Upper Limit = 250 + (1.96 * 75) = 397.
So, a shelter capacity of 350 will not be sufficient to house most abused women on 95% of all nights. The city's shelters would need 397 openings to meet this requirement.
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A national survey of 1000 adult citizens of a nation found that 15% dreaded Valentine's Day. The margin of error for the survey was 6.2 percentage points with 85% confidence. Explain what this means.
Answers
Answer:
We are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.
Step-by-step explanation:
Proportion of adults who dreaded valentines day = 15% = 0.15
The margin of error with 85% confidence = 6.2% = 0.062
The confidence interval is given by
p ± margin of error
0.15 ± 0.062
Lower limit = 0.15 - 0.062
Lower limit = 0.088
Lower limit = 8.8%
Upper limit = 0.15 + 0.062
Upper limit = 0.212
Upper limit = 21.2%
So it means that we are 85% confident that the proportion of adults who dreaded valentines day is within the range of 8.8% to 21.2%.
Triangle ABC is similar to Triangle FGH. What is the value of x in centimeters?
Answers
Given:
Given that the triangle ABC is similar to triangle FGH.
We need to determine the value of x.
Value of x:
Since, the triangles are similar, then their sides are proportional.
Thus, we have;
[tex]\frac{AC}{FH}=\frac{AB}{GF}=\frac{BC}{GH}[/tex]
Let us consider the proportion [tex]\frac{AB}{GF}=\frac{BC}{GH}[/tex] to determine the value of x.
Substituting AB = 9 cm, GF = 13.5 cm, BC = 15 cm and GH = x, we get;
[tex]\frac{9}{13.5}=\frac{15}{x}[/tex]
Cross multiplying, we get;
[tex]9x=15 \times 13.5[/tex]
[tex]9x=202.5[/tex]
[tex]x=22.5 \ cm[/tex]
Thus, the value of x is 22.5 cm
Hence, Option F is the correct answer.
Answer:
22.5
Step-by-step explanation:
what is 2/3 plus 1/6
Answers
Answer:
5/6
Step-by-step explanation:
2/3=4/6
4/6+1/6=5/6
Answer:
That would be 5/6
Step-by-step explanation:
You multiply the denominator and the numerator by 2 to get a common denominator of 6. You add the 4 to the 1 to get 5/6
A survey of an urban university (population of 25,450) showed that 883 of 1,112 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase
Answers
Answer:
The confidence interval for the proportion of students supporting the fee increase
( 0.77024, 0.81776)
Step-by-step explanation:
Explanation:
Given data a survey of an urban university (population of 25,450) showed that 883 of 1,112 students sampled supported a fee increase to fund improvements to the student recreation center.
Given sample size 'n' = 1112
Sample proportion 'p' = [tex]\frac{883}{1112} = 0.7940[/tex]
q = 1 - p = 1- 0.7940 = 0.206
The 95% level of confidence intervals
The confidence interval for the proportion of students supporting the fee increase
[tex](p-z_{\alpha } \sqrt{\frac{pq}{n} } ,p + z_{\alpha } \sqrt{\frac{pq}{n} } )[/tex]
The Z-score at 95% level of significance =1.96
[tex](0.7940-1.96\sqrt{\frac{0.7940 X 0.206}{1112} } ,0.7940 + 1.96 \sqrt{\frac{0.7940 X 0.206}{1112} } )[/tex]
(0.7940-0.02376 , 0.7940+0.02376)
( 0.77024, 0.81776)
Conclusion:-
The confidence interval for the proportion of students supporting the fee increase
( 0.77024, 0.81776)
4. Find the Area of the trapezoid.
Answers
Answer:
40 in^2
Step-by-step explanation:
The area of the trapezoid is found by
A = 1/2 (b1+b2)h where b1 and b2 are the lengths of the bases and h is the height
= 1/2 (7+3)*8
= 1/2 (10)*8
= 40 in^2
Answer:
ok the answer is 40
Step-by-step explanation:
a+b/2*h
7+3/2*8
7+3=10
10/2=5
5*8=40
Suppose that a manager is interested in estimating the average amount of money customers spend in her store. After sampling 36 transactions at random, she found that the average amount spent was $ 41.15 . She then computed a 90 % confidence interval to be between $ 38.01 and $ 44.29 .
Answers
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Step-by-step explanation:
Assuming this complete question: Which statement gives a valid interpretation of the interval?
The store manager is 90% confident that the average amount spent by the 36 sampled customers is between S38.01 and $44.29.
There is a 90% chance that the mean amount spent by all customers is between S38.01 and $44.29.
There is a 90% chance that a randomly selected customer will spend between S38.01 and $44.29.
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The 90% confidence interval for this case would be (38.01, 44.29) and is given.
The best interpretation for this case would be: We are 90% confident that the true average is between $ 38.01 and $ 44.29 .
And the best option would be:
The store manager is 90% confident that the average amount spent by all customers is between S38.01 and $44.29
A) A club is considering changing its bylaws. In an initial straw vote on the issue, 24 of the 40 members of the club favored the change and 16 did not. A committee of six is to be chosen from the 40 club members to devote further study to the issue. a) How many committees of six can be formed from the club membership
Answers
Answer:
38,38,380
Step-by-step explanation:
GIVEN: A club is considering changing its laws. In an initial straw vote on the issue, [tex]24[/tex] of the [tex]40[/tex] members of the club favored the change and [tex]16[/tex] did not. A committee of six is to be chosen from the [tex]40[/tex] club members to devote further study to the issue.
TO FIND: How many committees of six can be formed from the club membership.
SOLUTION:
Total number of members [tex]=40[/tex]
Total members to be chosen [tex]=6[/tex]
To select committee of [tex]6[/tex] members from [tex]40[/tex] [tex]=^{40}C_6[/tex]
[tex]=\frac{40!}{34!6!}[/tex]
[tex]=38,38,380[/tex]
Hence 38,38,380 different committee can be formed.
When conducting a significance test to determine if there is a difference between two treatments, with a quantitative response variable, treatments are given to different experimental units, we summarize the data by: Group of answer choices computing the proportion of the sample that reacted better to treatment one than treatment two. computing the mean and standard deviation of each treatment group separately. computing the difference in the responses for each experimental unit under both treatments, and then finding the mean and standard deviation of the differences. computing the difference in the proportion of the sample that reacted better to treatment one and the proportion of the sample that reacted better to treatment two.
Answers
Final answer:
To summarize data in a significance test for two different treatments with a quantitative response variable, the mean and standard deviation for each treatment group are computed separately to look for statistically significant differences.
Explanation:
When conducting a significance test to determine if there is a difference between two treatments with a quantitative response variable, and treatments are given to different experimental units, we summarize the data by computing the mean and standard deviation of each treatment group separately. This approach involves comparing the two sets of data from the treatment groups to see if there is a statistically significant difference in their means, which could suggest an effect of the treatments. This methodology is part of inferential statistics, where researchers use the collected sample data to make inferences about the population from which the sample was drawn.
We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 9 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size that we should consider
Answers
Answer:
The minimum sample size required is 25 so that margin of error is no more than 3 minutes.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 42 minutes
Standard Deviation, σ = 9 minutes.
We want to build a 90% confidence interval such that margin of error is no more than 3 minutes.
Formula for margin of error:
[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]
Putting values, we get.
[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}\leq 3\\\\1.64\times \dfrac{9}{\sqrt{n}}\leq 3\\\\\dfrac{1.64\times 9}{3}\leq \sqrt{n}\\\\4.92\leq \sqrt{n}\\\Rightarrow n\geq 24.2064\approx 25[/tex]
Thus, the minimum sample size required is 25 so that margin of error is no more than 3 minutes.
You are looking at the number of multi-million dollar companies in each state. Based on data from last year, you have found a mean of 37 and a standard deviation of 8. Use this information to answer the following question. What is the probability of a randomly selected state having between 21 and 53 multi-million dollars
Answers
Answer:
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
Step-by-step explanation:
We have no information about the distribution, so we use the Chebyshev's theorem to solve this question.
Chebyshev Theorem:
75% of the data within 2 standard deviations of the mean.
89% of the data within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 37
Standard deviation = 8
What is the probability of a randomly selected state having between 21 and 53 multi-million dollars
21 = 37 - 2*8
So 21 is 2 standard deviations below the mean.
53 = 37 + 2*8
So 52 is 2 standard deviations above the mean.
By the Chebyshev Theorem, 75% probability of a randomly selected state having between 21 and 53 multi-million dollars
50,866(underlined digits "66")
What is the relationship between
the underlined digits?
Answers
Answer:
6 at tens place is 10 times 6 at unit place.
Step-by-step explanation:
We are given that a number
50,866
Underlined digits are 66.
We have to find the relationship between underlined digits.
Unit place =6
Tens place=
Tens place value=[tex]6\times 10=60[/tex]
Unit pace value=6
6 at tens place is 10 times 6 at unit place.
This is required relation relation between underlined digits 66.
Let U ={1,2,3,4,5,6,7}, A={1,2,3,4}, and B ={1,2,4}. Find the set A intersection B
Answers
Answer:
its c I just id the test
Step-by-step explanation:
A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean?
A. [0.44,3.80]
B. [14.23,23.98]
C. [17.42,20.78]
D. [17.48,20.72]
Answers
Answer:
[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]
[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]
And the best option would be:
C. [17.42,20.78]
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=19.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=1.5 represent the sample standard deviation
n=9 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=9-1=8[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that [tex]t_{\alpha/2}=[/tex]
Now we have everything in order to replace into formula (1):
[tex]19.1-3.355\frac{1.5}{\sqrt{9}}=17.42[/tex]
[tex]19.1+3.355\frac{1.5}{\sqrt{9}}=20.78[/tex]
And the best option would be:
C. [17.42,20.78]