An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval

Answer:

The chi - square test can be [tex]\approx[/tex] 0.667

Step-by-step explanation:

From the given data :

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis: The number of customers does  follow  a uniform distribution

Alternative hypothesis: The number of customers does not  follow  a uniform distribution

We learnt that: Carl recorded the number of customers who visited his new store during the week:

Day              Customers

Monday               17

Tuesday              13

Wednesday         14

Thursday              16

The above given data was the observed value.

However, the question progress by stating that : He expected to have 15 customers each day.

Now; we can have an expected value for each customer  as:

                      Observed Value                   Expected Value

Day                 Customers                        

Monday                17                                          15

Tuesday               13                                          15

Wednesday          14                                          15

Thursday               16                                         15

The Chi square corresponding to each data can be determined by using the formula:

[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]

For Monday:

[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Tuesday :

[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Wednesday :

[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

For Thursday:

[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

                   Observed Value   Expected Value    chi - square

Day                 Customers                        

Monday                17                     15                       0.2666666667

Tuesday               13                     15                       0.2666666667

Wednesday          14                     15                       0.06666666667

Thursday               16                    15                       0.06666666667

Total :                                                                        0.6666666668

The chi - square test can be [tex]\approx[/tex] 0.667

At level of significance ∝ = 0.10

degree of freedom = n - 1

degree of freedom = 4 - 1

degree of freedom = 3

At ∝ = 0.10 and df = 3

The p - value for the chi - square test statistics is 0.880937

Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis

Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.

Answer:.67

Step-by-step explanation:

Answer:

a

  [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

b

  [tex]P( X >0.025 ) = 0.99379[/tex]

Step-by-step explanation:

From the question we are told that

   The  population proportion is  [tex]p = 0.10[/tex]

    The sample size is  [tex]n = 100[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]

=>   [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]

=>   [tex]SE =0.03[/tex]

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

   [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]

  Generally  [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]

   [tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]

From the z-table  

      [tex]P(Z < 2.6 ) = 0.99534[/tex]

     [tex]P(Z < 2.4 ) = 0.9918[/tex]

[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]  

 [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

        [tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]

        [tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]

From the z-table  

        [tex]P (Z > -2.5 ) = 0.99379[/tex]

Thus

      [tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

The  null hypothesis is  [tex]H_o : r < 0[/tex]

The  alternative hypothesis is  [tex]H_1 : r > 0[/tex]

Generally the standard deviation is mathematically evaluated as

       [tex]Sr = \sqrt{1- r}[/tex]

       [tex]Sr = \sqrt{1- 0.65}[/tex]

       [tex]Sr = 0.616[/tex]

The  degree of freedom for the one-tail test is

       [tex]df = n- 2[/tex]

        [tex]df = 14- 2[/tex]

        [tex]df = 12[/tex]

The standard error is evaluated as

        [tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]

        [tex]SE =0.1779[/tex]

The test statistics  is evaluated as

      [tex]t = \frac{r }{SE}[/tex]

       [tex]t = \frac{0.65 }{0.1779}[/tex]

        [tex]t = 3.654[/tex]

The p-value of of  t is obtained from the z table, the value is  

        [tex]p-value = P(t < 3.654) = 0.00012909[/tex]

Given that [tex]p-value < \alpha[/tex]  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

Step-by-step explanation:

[tex] \frac{x + 4}{3} = 2[/tex]

To solve it first of all cross multiply

That's

x + 4 = 6

Move 4 to the right side of the equation

The sign changes to negative

That's

x = 6 - 4

We have the final answer as

Hope this helps you

Answer:

The Variable has a coefficient.

Step-by-step explanation:

Answer:

C) w+4

Step-by-step explanation:

w=the variable

+4= increased by 4

HOPE THIS HELPS!!!!!! :)

<33333333333

Answer:

0

Step-by-step explanation:

0 because there is a $100 duty free exemption.

answer:

For this problem, use the tables and charts shown in this section.  

A United States Citizen returning to the States declares the following items at the customs office:

3 shirts at $8.50 each

2 dresses at $27.50 each

1 pair of gold cuff links at $17.50 per pair

If he has not used his duty free exemption yet, how much duty should he pay?

$0.00 !

$5.00

$10.00

$300

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

Answer:

Step-by-step explanation:

[tex]3h\left(2\right)+2k\left(3\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=3h\times \:2+2k\times \:3\\\\\mathrm{Multiply\:the\:numbers:}\:3\times \:2=6\\\\=6h+2\times \:3k\\\\\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6\\\\=6h+6k[/tex]

Answer:

Answers for E-dge-nuityyy

Step-by-step explanation:

(h + k)(2) = 5

(h – k)(3) = 9

Evaluate 3h(2) + 2k(3) = 17

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

=-2(x-5)(3x+2)

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

Slope = 5/1 = 5

Slope = 10/2 = 5

Slope = 15/3 = 5

Slope = 20/4 = 5

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

Read more about Linear function at; https://brainly.com/question/15602982

Answer:

2·5·5·5·5

Step-by-step explanation:

2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

=======================================================

Explanation:

Check out the diagram below.

Draw a vertical number line with 0 at the center. The positive values are above it, while the negative values are below it.

Between -15 and -16, closer to -16, plot the value -15.8 to indicate Ben's position. I have done so as the point B.

We move 4.2 units up to arrive at Cam's position

-15.8 + 4.2 = -11.6

So Cam is 11.6 meters below the surface of the water.

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:

Step-by-step explanation:

x^2+20=4 first isolate the variable by subtracting 20 on both sides.

x^2=-16 again isolate the variable but this time you square root both sides.

[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify

x= ±4

Answer:

d

Step-by-step explanation:

(-7 + 3i) + (2-6i)

=-7 + 3i + 2 -6i

=(-7+2) + (3i -6i)

=-5 -3i

Answer:

(-7+3I)+(2-6I)

= -7+3i+2-6i

= -5-3I

so answer is d ie -5-3i

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Step-by-step explanation:

We are given the following hypothesis below;

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9      {means that the population mean is equal to 88.9}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9     {means that the population mean is different from 88.9}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 81.3

             s = sample standard deviation = 13.4

            n = sample size = 7

So, the test statistics =  [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex]   ~ [tex]t_6[/tex]

                                     =  -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

                    P-value = P([tex]t_6[/tex] < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.