According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned (BusinessWeek, January 1 5, 2007). A Houston department store sampled 80 items sold in January and found that 12 of the items were returned.Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.

Answers

Answer 1

Answer:

Using the sample proportion, it is found that the point estimate is of 0.15 = 15%.

What is a sample proportion?

A sample proportion is given by the number of desired outcomes divided by the number of total outcomes. It can also serve as the point estimate for the population proportion.

In this problem, 12 out of the 80 items sold were returned, hence:

12/80 = 0.15 = 15%.

The point estimate is of 0.15 = 15%.

More can be learned about point estimates at brainly.com/question/24651197

Answer 2

Answer:

Answer:

a) $\hat p = (X)/(n)= (12)/(80)= 0.15$

b) $0.15 - 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.072$

$0.15 + 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.228$

And the 95% confidence interval would be given (0.072;0.228).

c) For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

Step-by-step explanation:

Assumign the following question for the problem:

a. Construct a point estimate of the proportion of items returned for the population of sales transactions at the Houston store.

For this case the best estimate for the true proportion is given by the sample proportion:

$\hat p = (X)/(n)= (12)/(80)= 0.15$

b. Construct a 95% confidence interval for the porportion of returns at the Houston store.

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".

The confidence interval would be given by this formula

$\hat p \pm z_(\alpha/2) \sqrt{(\hat p(1-\hat p))/(n)}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=1.96$

And replacing into the confidence interval formula we got:

$0.15 - 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.072$

$0.15 + 1.96 \sqrt{(0.15(1-0.15))/(80)}=0.228$

And the 95% confidence interval would be given (0.072;0.228).

c. Is the proportion of returns at the Houston store significantly different from the returns for the nation as a whole? Provide statistical support for your answer.

For this case since the confidence interval not contains the value 0.06 or 6% and since the lower limit for the confidence interval is higher than 0.06 (0.072>0.06), we have enough statistical evidence to support the conclusion that the true proportion of items returned is higher than 0.06 or 6% at a significance of 5%.

Related Questions

the radius of the cone is 1.75 inches, and it’s height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
what are the steps for multiplying monomial algebraic terms where they have exponents with like bases
The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?
1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a? 2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)? 3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g? 4. If f(x) is a polynomial, is f(x^2) also a polynomial 5. Consider the polynomial function g(x) = x^4-3x^2+9 a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial
Materials: Tall clear drinking glass or vase At least four of the following liquids: Fresh water Salt water Vegetable oil Rubbing alcohol Dish soap Honey Corn syrup Milk Maple syrup At least three different small items of your choice, such as: Ping pong ball Small screw, bolt, or nut Popcorn kernel Peanut Blueberry Grape Cherry tomato Instructions: Select four liquids and predict how you think they compare in density by ranking them from most dense to least dense in the data table below. Measure out ¼ cup volume of each liquid, and pour them one at a time into the clear glass or vase. Record your observations in the lab worksheet. Gently add the first small item to the liquids, and record your observation of where it settles. Repeat with the other small items. Clean up all lab materials (the liquids can be poured down the sink), and complete the lab worksheet. Data Table: Prediction: Rank the four liquids from lowest density (top) to highest density (bottom) Observation: Rank how the four liquids really compare, from lowest density (top) to highest density (bottom) Observations: What objects did you place in the liquid, and where did each settle? Object Layer where it settled Observations and Conclusions: Define density, and describe how this activity helps you compare the density of four different liquids without making mass measurements. How did the observations compare to your predictions? Did any of the results surprise you? How would the density of water change if you measured out ½ cup instead of ¼ cup? Explain your answer in complete sentences.

Rick and Tom rented party halls. The Celebrations party hall charged Rick a rental fee of $65, including music, and $25 per guest. The Feast party hall charged Tom a rental fee of $40, $25 for music, and $25 per guest.If each of them spent the same amount of money, how many guests attended Rick and Tom's party?

A.
Five more guests attended Rick's party than Tom's party.
B.
Fifteen more guests attended Tom's party than Rick's party.
C.
The same number of guests attended Rick and Tom's party.
D.
Twenty-five more guests attended Rick's party than Tom's party.

Answers

Answer:

C. The same number of guests attended Rick and Tom's party.

Step-by-step explanation:

Let R and T represent the number of guests at Rick's and Tom's parties, respectively. The charges Rick and Tom paid are equal, so we have ...

65 +25R = 40+25+25T

25R = 25T . . . . . . . . . . . . subtract 65

R = T . . . . . . . . . . . . . . . . . divide by 25

The number of guests at each party is the same.

7h + 10 = 9h + 4

A. h=3

B. h=4

C. h=5

D. h=6

Answers

Answer:

A. h=3

Step-by-step explanation:

soln

7h + 10 = 9h + 4

then you correct like terms together

9h - 7h = 10 - 4

2h = 6

2 2

h = 3

the is A

Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers?At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].(c) What does the First Derivative Test tell you that the Second Derivative test does not? (Enter your answers from smallest to largest x value.)At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].At x = the function has ---Select--- [a local minimum, a local maximum, or neither a minimum nor a maximum].

Answers

Answer:

$a) x=0, x=(12)/(11), x=2 \:$ b) The 2nd Derivative test shows us the change of sign and concavity at some point. c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

Step-by-step explanation:

a) To find the critical numbers, or critical points of:

$f(x)=x^(6)(x-2)^(5)$

1) The procedure is to calculate the 1st derivative of this function. Notice that in this case, we'll apply the Product Rule since there is a product of two functions.

$f(x)=x^(6)(x-2)^(5)\Rightarrow f'(x)=(f*g)'(x)\n=f'g+fg'\Rightarrow (fg)'(x)=6x^(5)(x-2)^(5)+5x^(6)(x-2)^(4) \Rightarrow 6x^(5)(x-2)^(5)+5x^(6)(x-2)^(4)=0\nf'(x)=6x^(5)(x-2)^(5)+5x^(6)(x-2)^(4)$

2) After that, set this an equation then find the values for x.

$x^(5)(x-2)^(4)[6(x-2)+5x]=0\Rightarrow x^(5)(x-2)^(4)[11x-12]=0\Rightarrow x_(1)=0\n(x-2)^(4)=0\Rightarrow \sqrt[4]{(x-2)}=\sqrt[4]{0}\Rightarrow x-2=0\Rightarrow x_(2)=2\n(11x-12)=0\Rightarrow x_(3)=(12)/(11)$

$x=0\:(smallest\:value)\:x_(3)=(12)/(11)\:x=2 (largest value)$

b) The Second Derivative Test helps us to check the sign of given critical numbers.

Rewriting f'(x) factorizing:

$f'(x)=(11x-12)(x-2)^4x^(5)$

Applying product Rule to find the 2nd Derivative, similarly to 1st derivative:

$f''(x)>0 \Rightarrow Concavity\: Up\n\nf''(x)<0\Rightarrow Concavity\:down$

$f''(x)=11\left(x-2\right)^4x^5+4\left(x-2\right)^3x^5\left(11x-12\right)+5\left(x-2\right)^4x^4\left(11x-12\right)\nf''(x)=10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)$

1) Setting this to zero, as an equation:

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\n\n$

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\n(x-2)^(3)=0 \Rightarrow x_1=2\nx^(4)=0 \therefore x_2=0\n11x^(2)-24x+12=0 \Rightarrow x_3=(12+2√(3))/(11)\:,x_4=(12-2√(3))/(11)\cong 0.78$

2) Now, let's define which is the inflection point, the domain is as a polynomial function:

$D=(-\infty<x<\infty)$

Looking at the graph.

Plugging these inflection points in the original equation $f(x)=x^(6)(x-2)^(5)$ to get y coordinate:

We have as Inflection Points and their respective y coordinates (Converting to approximate decimal numbers)

$(1.09,-1.05)$ Inflection Point and Local Minimum

$(2,0)$ Inflection Point and Saddle Point

$(0,0)$ Inflection Point Local Maximum

(Check the graph)

c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

$x=(12)/(11)\cong1.09$ Local Minimum

$At\:x=0,\:Local \:Maximum$

$At\:x=2, \:neither\:a\:minimum\:nor\:a\:maximum$ (Saddle Point)

Final answer:

To find the critical numbers of the function f(x) = x^6(x - 2)^5, we need to set the first derivative equal to zero and solve for x. The Second Derivative Test tells us the behavior of the function at the critical numbers, while the First Derivative Test tells us the behavior of the function based on the sign change of the derivative at the critical numbers.

Explanation:

The critical numbers of the function f(x) = x^6(x - 2)^5 can be found by taking the first and second derivatives of the function. The first derivative is f'(x) = 6x^5(x - 2)^5 + 5x^6(x - 2)^4 and the second derivative is f''(x) = 30x^4(x - 2)^5 + 20x^5(x - 2)^4.

To find the critical numbers, we need to set the first derivative equal to zero and solve for x: 6x^5(x - 2)^5 + 5x^6(x - 2)^4 = 0. We can solve this equation using factoring or by using the Zero Product Property. Once we find the values of x that make the first derivative zero, we can evaluate the second derivative at those values to determine the behavior of the function at those critical numbers.

The Second Derivative Test tells us that if the second derivative is positive at a critical number, then the function has a local minimum at that point. If the second derivative is negative at a critical number, then the function has a local maximum at that point. If the second derivative is zero, the test is inconclusive and we need to use additional information to determine the behavior of the function. The First Derivative Test tells us that if the derivative changes sign from negative to positive at a critical number, then the function has a local minimum at that point. If the derivative changes sign from positive to negative at a critical number, then the function has a local maximum at that point.

Learn more about Critical numbers and behavior of functions here:

brainly.com/question/34150405

#SPJ3

Compute the permutation. 30 P 3
Answer options: 9,000 27,000 24,360

Answers

Answer:

24,360

Step-by-step explanation:

30P3 = 30!/(30-3)! = 30·29·28 = 24,360

Answer:

Compute the permutation. 30 P 3

Answer options: 9,000 27,000 24,360

Step-by-step explanation:

The factorial function (symbol:!) Means that descending numbers are multiplied. 30 P 3.

30! = 30 x 29 x 28 =24,360

The answer is: 24,360

|-9×+7|+8 is less than or equal to 9

Answers

Answer:

I don’t think it’s neither less than it equal

Step-by-step explanation:

I could be wrong don’t listen to me :)

List all the factor pairs for 48 make a tabletop to help

Answers

1 and 48 are a factor pair of 48 since 1 x 48= 48

2 and 24 are a factor pair of 48 since 2 x 24= 48

3 and 16 are a factor pair of 48 since 3 x 16= 48

4 and 12 are a factor pair of 48 since 4 x 12= 48

6 and 8 are a factor pair of 48 since 6 x 8= 48

8 and 6 are a factor pair of 48 since 8 x 6= 48

12 and 4 are a factor pair of 48 since 12 x 4= 48

16 and 3 are a factor pair of 48 since 16 x 3= 48

24 and 2 are a factor pair of 48 since 24 x 2= 48

48 and 1 are a factor pair of 48 since 48 x 1= 48

Other Questions

Pls do this for me I am getting annoyed with this

When Jack, Jill, and Bill each came down the hill carrying a 48-ouncebucket full of water. By the time they reached the bottom, Jack's bucket was only 3/4 full. How much water did Jack spill? 14 oz. O 12 oz. O 3/48 oz 16 oz. Plz HELPPPP AGIAN

Edwin raps for 10 minutes on Monday. On Tuesday he raps for anhour. Find out how many minutes he has practiced so far this week.

Which type of angle is formed by sides of a square?