The changes in housing prices over short time periods are in part determined by supply and demand. A real estate company in Minnesota projected an increase in its average selling prices of homes in the first quarter of 2014 over the mean 2013 selling price of $201,800. The reason for the projection was an increase in demand due to business expansion and the subsequent increase in labor. To investigate the accuracy of the projection, a sample of homes in the first quarter of 2014 was selected and the following selling prices (in $) recorded:

235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500

Required:
a. At 5% level of significance, is there sufficient evidence to support the real estate company's projection?
b. Which statistical distribution should be applied in this situation and why? Explain carefully.
c. Discuss the consequences of Type I and Type II errors in terms of the problem.
d. Does the management at the real estate company want a small or large value of the significance level? Explain carefully.
e. Based on a 95% confidence level, estimate the actual average selling price homes in the first quarter of 2014.

Answers

Answer 1

Answer:

The data given is  

    235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500

  The sample size is  n =  16

   The population is  [tex]\mu  =  \$201,800[/tex]

  The sample mean is mathematically represented as

             [tex]\= x =\frac{\sum x_i}{n}[/tex]

=>  [tex]\= x  =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}[/tex]

=>    [tex]\= x  = 218653.125[/tex]

Generally the sample standard deviation is mathematically represented as

     [tex]s =  \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]

=>   [tex]s =  \sqrt{\frac{ (235,000 -  218653.125)^2+ (271,900 -  218653.125)^2 + \cdots +  (245,500 -  218653.125)^2}{16} }[/tex]

=>   [tex]s =  23946.896 [/tex]

The null hypothesis is  [tex]H_o : \mu =  \$201,800[/tex]

The alternatively hypothesis is  [tex]H_o : \mu >  \$201,800 [/tex]

Generally the test statistics is mathematically represented as

     [tex]t =  \frac{\= x  - \mu }{ \frac{s}{\sqrt{n} } }[/tex]

=>  [tex]t =  \frac{218653.125  - 201800 }{ \frac{23946.896 }{\sqrt{16} } }[/tex]

=>  [tex]t =  2.82[/tex]

Generally the degree of freedom is mathematically represented as

     [tex]df =  n - 1[/tex]

=>   [tex]df =  16 - 1[/tex]

=>   [tex]df =  15[/tex]

Generally the probability of  [tex]t =  2.82[/tex] at a degree of freedom of  [tex]df =  15[/tex] from the t - distribution table  is  

     [tex]p-value  = P( t >2.82 ) =0.00646356[/tex]

The

From the values obtained we see that [tex]p-value  < \alpha[/tex]

The decision rule is  

   Reject the null hypothesis

The conclusion is

 There is sufficient evidence to conclude that the real estate company's  projection is true

Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution

Type I  Error

 The type 1 error occur when the null hypothesis is wrongfully rejected

  The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still  $201,800

   Type II  Error

 The  type 11 error occur when the null hypothesis is wrongfully  accepted(i.e wrongfully failed to reject the null hypothesis)

    The consequence in this case is that the company will assume that the average selling price  is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased

   Given that resource is scare the management of the company will want a  smaller  significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources

generally the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is    

     [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

   [tex]E  =Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }[/tex]

=>[tex]E  =1.96*  \frac{23946.896}{\sqrt{16} }[/tex]

=>[tex]E  = 11733.96[/tex]

Generally the 95% confidence interval is  mathematically represented as

     [tex]218653.125 - 11733.96  < \mu  <  218653.125 + 11733.96[/tex]

=>  [tex]206919.165  < \mu  <  230387.085[/tex]  

Generally there is 95% confidence that the actual average selling price is within this interval  

Step-by-step explanation:


Related Questions

Water flows through a pipe at a rate of 710 pints per day. Express this rate of flow in cubic feet per month.

Answers

Answer:

355.923 cubic feet per month

Step-by-step explanation:

Units Conversions

We need to convert from pints/day to cubic feet/month. Two basic conversions are needed:

1 US pint = 0.0167101 cubic foot

1 month = 30 days (average)

710 pints are equivalent to 710 * 0.0167101 = 11.8641 cubic feet

That volume corresponds to a daily flow. For a monthly flow, multiply by 30:

355.923 cubic feet per month

KOT
2
1013
67
Motorcycle
Walking100
a) How many students ride in a tricycle, motorcycle and car going to their school
b) How many students ride in both a motorcycle and a tricycle?
c) How many students ride in both a motorcycle and a car?
d) How many students ride in both a car and tricycle?
e.)How many students go to school
in a car only;
in a motorcycle only;
30

Answers

Answer:

a. 15 students

b. 32 students

c. 35 students

d. 34 students

e. 55 students

f. 67 students

Step-by-step explanation:

See attachment for complete question

Solving (a): Tricycle, Motorcycle and Car

This is the intersection of Tricycle, Motorcycle and Car.

From the attached Venn diagram, there are 15 students in this category

Solving (b): Tricycle and Motorcycle.

This is the intersection of Tricycle and Motorcycle.

From the attached Venn diagram, we observe the following data:

[tex]Tricycle\ and\ Motorcycle\ only =17[/tex]

[tex]All = 15[/tex]

[tex]Tricycle\ and\ Motorcycle = All + Tricycle\ and\ Motorcycle\ only[/tex]

[tex]Tricycle\ and\ Motorcycle = 15 + 17[/tex]

[tex]Tricycle\ and\ Motorcycle = 32[/tex]

Solving (c): Car and Motorcycle.

This is the intersection of Car and Motorcycle.

From the attached Venn diagram, we observe the following data:

[tex]Car\ and\ Motorcycle\ only = 20[/tex]

[tex]All = 15[/tex]

So:

[tex]Car\ and\ Motorcycle = All + Car\ and\ Motorcycle\ only[/tex]

[tex]Car\ and\ Motorcycle = 15 + 20[/tex]

[tex]Car\ and\ Motorcycle = 35[/tex]

Solving (d): Car and Tricycle.

This is the intersection of Car and Tricycle.

From the attached Venn diagram, we observe the following data:

[tex]Car\ and\ Tricycle\ only = 19[/tex]

[tex]All = 15[/tex]

So:

[tex]Car\ and\ Tricycle = All + Car\ and\ Tricycle\ only[/tex]

[tex]Car\ and\ Tricycle = 15 + 19[/tex]

[tex]Car\ and\ Tricycle = 34[/tex]

Solving (e): Car only

From the attached Venn diagram, we observe the following data:

[tex]Car\ only = 55[/tex]

Solving (e): Motorcycle only

From the attached Venn diagram, we observe the following data:

[tex]Motorcycle\ only = 67[/tex]

20. Bob had 7/8 pack of construction paper. If he used 1/5 of the paper to 5 points
make a paper plane, how many WHOLE paper planes could he make? *

Answers

Answer:

3

Step-by-step explanation:

he has 7/8 paper divided by 1/5 paper it takes to make the paper plane, it equals 3.5. Three whole ones

Melissa needs 3.87 feet of string to use as a border for her poster. Melissa finda a piece of string that is is 4.25 feet long. how much string will Melissa have left over​

Answers

Answer:

You will have .38 feet left of string

Step-by-step explanation:

Just subtract the numbers

Have a good day!

Answer:

0.38

Step-by-step explanation:

4.25-3.87=0.38

A giant garter snake is at least 64 inches long. If 1 inch is equal to
2.5 cm, how long is the Giant garter snake in cm?

Answers

Answer:

The snake would equal 160cm.

Step-by-step explanation:

Correct me if im wrong plz

what is -3/8 ÷ 7/12 help

Answers

Answer:

-9/14

Step-by-step explanation:

Have a good day <3

Answer:

-9/14

Step-by-step explanation:

-3/8 ÷ 7/12

Flip the second fraction and multiply

-3/8 x 12/7

You can cross-simplify

-36/56

-9/14

Hope this helped!

Solve:
5x + 10 = -15

Answers

X=-5
Pls mark me brainliest

Answer:

x= -5

Step-by-step explanation:

5x + 10 = -15

subtract 10 from both sides

5x = -25

divide both sided by 5

x = -5

Hope this helps :)

According to modern science. Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose you represent the entire history of Earth by 12 hours on a clock, with the birth of Earth at the stroke of midnight and today at the stroke of noon. How long before noon does written human history begin?

Answers

Answer:

11:59:59. Human history can be represented as only less than one second in a 12 hour clock.


Jeannine puts 10% of her paycheck into a savings account. If she makes $500 each week,
how much does she put in her savings account each week?

Answers

Answer:

$50

Step-by-step explanation:

divide 500 by 10, which is 50 so $50

Labor costs. Labor costs for a farmer are $55 per acre for corn and $45 per acre for soybeans. How many acres of each crop should the farmer plant if he wants to spend no more than $6,900 on labor?

Answers

Answer:

392984

Step-by-step explanation:

Given the function d (t) = 50t, the variable t represents which of the following
Output
Independent variable
Function
Input
Depended variable

Answers

Answer:

The input of the function

Step-by-step explanation:

You can buy 3 apples at the City Market for $1.20. You can buy 5 of the same apples at Shop and Save for $2.10. Which place is the better buy?

Answers

Answer:

Shop and save

Step-by-step explanation:

Answer:

You can buy 5 of the same apples at Shop and Save for $2.10.

Step-by-step explanation:

Simplify the expression:
27
simplifying square roots

Answers

Answer:

3^2

Step-by-step explanation:

3x3x3 = 27

Because if you have 3^2 then that is 3 to the power of 2 and 3 to the power of 2 is 27.

Answer:

3 by the power of 2

Step-by-step explanation:

Solve for j if aj+k=v

Answers

Answer:

j=v-k/a

Step-by-step explanation:

It's like order of operations backwards. So first, you would get rid of the k, by subtracting it from both sides. Then, to isolate j you would divide both sides by a.


Factorise fully
10c + 25​

Answers

Answer:

5(2c+5)

I hope this helps

A study was being conducted about birth weights of babies at a local hospital and found the average to be 7.6 pounds with a standard deviation of 1.3 pounds (the distribution was approximately normal). Many pre-mature births weights are in the lowest 1% of births. What would be the birth weight associated with the lowest 1%?

Answers

Answer:

The birth weight associated with the lowest 1% is 4.6 pounds.

Step-by-step explanation:

Let X represent the birth weights of babies.

It is provided that [tex]X\sim N(7.6,1.3^{2})[/tex]

It is also provided that many pre-mature births weights are in the lowest 1% of births.

Let x represent the births weights that are in the lowest 1% of births.

That is, P (X < x) = 0.01.

⇒ P (Z < z) = 0.01

The corresponding z-score is, z = -2.33.

Compute the value of x as follows:

[tex]z=\frac{s-\mu}{\sigma}\\\\-2.33=\frac{x-7.6}{1.3}\\\\x=7.6-(1.3\times 2.33)\\\\x=4.571\\\\x\approx 4.6[/tex]

Thus, the birth weight associated with the lowest 1% is 4.6 pounds.

5+(-5)=0 identify the property

Answers

Answer: Additive Inverse

Step-by-step explanation: The Additive Inverse tells us that if we add

a number and the opposite of that number, the result will be 0.

insert 6A.M's between 15 and -13​

Answers

Answer:

-13

Step-by-step explanation:

see if good

488 points for defeating 61 enemies

Answers

Divide 488 by 61 to find the unit rate.

488/61 = 8

You get 8 points for defeating each enemy.

Hope this helps

Write 3.4 times 10^-2

Answers

3.4% divided by 14 39$:&;6;$;$&;!;$;$

Answer:

0.034

Step-by-step explanation:

10^-2 is 1 over 100 times 3.4

Regina used nuts and fruits to make a snack mix. The graph below shows the quantities used for each serving

What do the points on the graph mean in this context? Select all that apply.

For every 3 cups of fruit, there is 1 cup of nuts.

For every 1 cup of fruit, there are 3 cups of nuts.

For every 2 cups of fruit, there are 6 cups of nuts.

For every 6 cups of fruit, there are 2 cups of nuts.

For every 12 cups of fruit, there are 4 cups of nuts.

Answers

Answer: 1st, 4th & 5th .

Answer:

1st, 4th, and 5th

Step-by-step explanation:

FIRST RIGHT GETS BRAINLIEST. Find the decimal and Percent of 2/3

Answers

Answer:

0.667 and 66.67% rounded

Step-by-step explanation:

2/3 = 0.66666 repeating which can be rounded to 0.667

2/3 = 66.6666% repeatinf which can be rounded to 66.67%

                                    _

Answer: Decimal = 0.6  Percent = 66.67%

Step-by-step explanation: The line above the 6 in 0.6 stands that it repeats over and over again, and the percent is 66.67% because if you divide 100/3x2, you get 66.67.

Please answer quickly I really need this answer

Answers

D - 10

hope this helps :)

Answer:

The answer is 10

Keri has a spinner with sections labeled Black,
Blue, Orange, and Purple. What is the
theoretical probability of Keri spinning the
spinner and landing on blue or black?

Answers

Answer:

50%

Step by step explanation

100 divided by 4 is 25

Since it is both blue and black, it is doubled from 25 to 50

What is the slope of the line graphed below?

Answers

The slope is -3/2.....

y = x²+1 at x=1 what’s the solution?

Answers

y = x^2 + 1
if x = 1 then
y = 1^2 + 1 ( 1^2 = 1 )
y = 1 + 1
y = 2

A linear function f models a relationship in which the dependent variable decreases 3 units for every 2 units the independent variable increases. The value of the function at 0 is -5. Identify the slope, y-intercept, and x-intercept of the graph.
FULL EXPLANATION PLEASE.

Answers

Answer:

this is your question

Step-by-step explanation:

please mark as brainliest

The slope of the linear function would be 1/6, [y] - intercept will be equal to -5 and [x] - intercept will be equal to 1/30.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have a linear function f(x) that models a relationship in which the dependent variable decreases 3 units for every 2 units the independent variable increases. The value of the function at 0 is -5

Since the dependent variable decreases 3 units for every 2 units the independent variable increases, we can write -

3y = 1/2x

y = 1/6x

At [x] = 0, y = - 5

So -

y = (1/6)x - 5

Now -

slope = 1/6

[y] - intercept = - 5

y = 0 = (1/6)x - 5

(1/6)x - 5 = 0

1/6x = 5

x = 1/30

[x] - intercept = 1/30

Therefore, the slope of the linear function would be 1/6, [y] - intercept will be equal to - 5 and [x] - intercept will be equal to 1/30.

To solve more questions on Money and taxes, visit the link below-

https://brainly.com/question/4448868

#SPJ2

find m ABC (2x) (5x+5)

Answers

Answer:

=130

Step-by-step explanation:

(2x) (5x+5) = 180

7x + 5 = 180

7x = 175

x = 25

5(25) + 5 = 125 + 5 = 130

Hope this helps (:

Write an algebraic expression for 27 less than a number.

Answers

Answer:

n-27

Step-by-step explanation:

If we assume the number is n, the expression will be n-27. You could use any other variable, too. Hope it helps!

Answer:

f - 27

Step-by-step explanation:

we don't know the number that's being subtracted so it would be any integer minus 27

two numbers or expressions that have been the same value are

Answers

Answer:

equivalent

Step-by-step explanation:

Equivalent means equal so equivalent expressions equal the same value.

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