Sales commissions: A company studied two programs for compensating its sales staff. Nine salespeople participated in the study. In program , salespeople were paid a higher salary, plus a small commission for each item they sold. In program , they were paid a lower salary with a larger commission. Following are the amounts sold, in thousands of dollars, for each salesperson on each program

Salesperson
Program 1 2 3 4 5 6 7 8 9
A 55 22 34 22 25 61 55 36 68
B 53 24 36 28 31 61 58 38 72

Required:
Can you conclude that the mean sales differ between the two programs? Use the α = 0.05 level of significance

Answers

Answer 1

Using the t-distribution, it is found that since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.

At the null hypothesis, it is tested if the mean sales do not differ between the two programs, that is, the subtraction of the means is 0, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if they differ, that is:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

The mean and the standard errors for each sample are:

[tex]\mu_1 = 42, s_1 = 5.9675[/tex]

[tex]\mu_2 = 44.56, s_2 = 5.6177[/tex]

The distribution of the difference has mean and standard deviation given by:

[tex]\overline{x} = \mu_2 - \mu_1 = 44.56 - 42 = 2.56[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{5.9675^2 + 5.6177^2} = 8.1957[/tex]

The test statistic is:

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

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Then:

[tex]t = \frac{2.56 - 0}{8.1957}[/tex]

[tex]t = 0.31[/tex]

The critical value for a two-tailed test, as we are testing if the mean is different of a value, with 9 + 9 - 2 = 16 df and a significance level of 0.05 is [tex]|t^{\ast}| = 2.12[/tex]

Since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.

A similar problem is given at https://brainly.com/question/13873630


Related Questions

Find the average of the following numbers: 55.1, 67.9, 59.2, 64.1, 61.8, 62.7. Round
your answer to one decimal place *
Your answer

Answers

Answer:

61.8

Step-by-step explanation:

[tex] \frac{55.1 + 67.9 + 59.2 + 64.1 + 61.8 + 62.7}{6} [/tex]

61.8 is the answer to 55.5 576

you throw a football straight up into the air with a speed of 12.2m/s. How high those the ball go?

Answers

Answer:

7.6m

hope this helps :)

Math expert please simplify this I am confuse thanks you

Answers

Answer:

11

Step-by-step explanation:

39 - 6 / 3

= (39 - 6) / 3

= 33 / 3

= 11

Answer:

a-2

Step-by-step explanation:

(3a-6)/3 You can factor the numerator to 3(a-2) so you have

[tex]\frac{3(a-2)}{3}[/tex]

simply divide by the 3->

a-2

The number of fish in a lake decreased by 15% between last year and this year. This year, there were 51 fish in the lake. What was the population last year? Consider creating a tape diagram, to help you make sense of the situation.​

Answers

Answer:

234

Step-by-step explanation:

the d of c e rt rt egr yr oigj rethoy ejtheruot  utheoig  eoigh eoijg oeijrg ioetjg eroitj e eiotj  ertioj wet df fv 1q3r  2396 e059i58 the end oej etejg rtyehr

The answer to your question is 7.65.

What is the range for this data set?
22, 7, 14, 13, 38, 12, 19,
17, 49, 13, 9, 18, 36​

Answers

Answer:

from 7 to 49 or (7, 49)

Step-by-step explanation:

Range means the limit of the data set. Basically, the low part of the range is the lowest number in the set and the high part of range is the highest part.

4(4 + 7x) + x 2 -6x +5

Answers

Factoring this equation would get you (x+21)(x+1)

2x-3y=5.5
What is the solution to the system of equations shown above

Answers

Answer:

⸻⸻⸻⸻⸻

Solving

2X + 3Y = 5.5

⸻⸻⸻⸻⸻

Simplifying

2X + 3Y = 5.5

⸻⸻⸻⸻⸻

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

⸻⸻⸻⸻⸻

Add -3y to each side of the equation.

2x + 3y + -3y = 5.5 + -3y

⸻⸻⸻⸻⸻

Combine terms: 3y + -3y = 0.

2x + 0 = 5.5 + -3y

2x = 5.5 + -3y

⸻⸻⸻⸻⸻

Divide each side by 2.

x = 2.75 + -1.5y

⸻⸻⸻⸻⸻

Simplifying.

x = 2.75 + -1.5y

⸻⸻⸻⸻⸻

Help help help help help help help

Answers

Answer:

(1,1)0that is the answer I think

Answer:

A = 1,1 B = 4,2 C = 2,4

Explanation:

90 cw (270 ccw) - Same y, opposite x.

180 - opposite x, opposite y

270 cw (90 ccw) - opposite y, same x

A rectangular field is ten times as long as it is wide. If the perimeter of the field is 1100 feet, what are the dimensions of the field?

Answers

Answer:

Length = 500, Width = 50

Step-by-step explanation:

EQUATION:

2(10x) + 2x = 1100

20x + 2x = 1100

22x = 1100

x=50

Graph the set of real numbers on a number line. {x|-3 < x and x< 1}

Answers

Answer:

9

Step-by-step explanation:

8000000000000

9

0

9

In Martin's class of 20 students, 4 students report that social studies is their favorite class and 75% of the students report that PE is their favorite class. Show your work to explain how to determine whether more students prefer social studies or PE. (5 points)
pls Help!

Answers

Answer:

More students like PE

Step-by-step explanation:

100÷20=5

1 student = 5%

4×5=20

20% students favourite is social studies

75%>20%

7. Veronica brought her turtle out of its aquarium for 15 minutes every
night for 7 days. How many total minutes did she bring her turtle
out of its aquarium? Write another scenario that uses the same numbers.



Help me plz I know the answer, but I need help writing another scenario that uses the same numbers.

Answers

Answer:

Brittany took a 15 minute walk every morning for 7 days. How many minutes did she walk for?

Step-by-step explanation:

You might be able to use this.

Which equation represents a circle whose center is (3,-1) and whose radius is V6?​

Answers

Step-by-step explanation:

(Pie)r^2 that is the area of a circle

Simplify the expression.5(z+4)+5(2−z)

Answers

Answer:

30

Step-by-step explanation:

Hope this helps!!! :))

68% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number of US adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, (c) less than four.

Answers

Answer:

A) 12.29%

B) 81.33%

C) 1.55%

Step-by-step explanation:

This is a binomial model, and I assume you're meant to use a calculator to solve.

A)

This is what I have in my notes for the binompdf function:

binompdf(n, p, x) - find the probability of exactly x successes in n trials given p probability

That is exactly what we want in this case, we're looking for exactly 5 people who meet the conditions (successes) given n trials and p probability.

Using a calculator:

binompdf(10, 0.68, 5) ≈ 0.1229

That means you have about a 12.29% chance to randomly select exactly 5 adults who have little confidence in newspapers.

B)

For this one, use the binomcdf function:

binomcdf(n, p, x) - find the probability of x or fewer successes in n trials given p probability

In this case, we're looking for more, not less. However, you can think of the probability of getting more than 6 as just the probability of not getting less than 6.

With a calculator:

binomcdf(10, 0.68, 5) ≈ 0.1867

That means you have about an 18.67% chance to randomly select 5 or less people. We're looking for more though. As said above, the probability of getting 6 or more is just the probability of not getting 5 or less. To find the probability of something not happening, just subtract the probability from 1.

1 - 0.1867 = 0.8133

An 81.33% chance to randomly select at least 6 adults who have little confidence in newspapers.

C)

Same as the above, I don't see a need to explain it all again. Use binomcdf:

binomcdf(10, 0.68, 3) = 0.0155

Notice I used 3 rather than 4. binomcdf calculates x or fewer, or 'rather less than or equal to'. We want just 'less than 4', and that means 'less than or equal to 3'.

That's a 1.55% chance to select less than 4 adults with little confidence in newspapers.

Simplify the liner expression
−2/3a+1/8−1/6a−3/4

Answers

This is how far you can simplify it

I need help with b .

Answers

Answer:

Finding a common denominator is the same as finding a common multiple. You can multiply the denominators by each other, or list out the multiples of each denominator. Multiplying by others' unique factors gives the least common denominator.

Cuál es la altura (h) del velero

Answers

The answer is 8.72, the question is on the internet

Utilizando propiedades de triángulos rectángulos, veremos que la altura h es igual a 4.28m

Lo primero que debemos notar es que tenemos un triangulo rectángulo. En el podemos ver un ángulo de 55°.

El cateto adyacente tiene una longitud de 3m, y queremos obtener la longitud del cateto opuesto.

Podemos usar la relación trigonométrica:

Tan(θ) = (cateto opuesto)/(cateto adyacente)

Reemplazando los valores que conocemos, obtendremos:

Tan(55°) = h/3m

Tan(55°)*3m = h = 4.28m

La altura h del velero es 4.28m

Sí quieres aprender más, puedes leer:

https://brainly.com/question/22050734

The walls and ceiling of a hotel room are to be painted. The ceiling is a 22-foot square, and the walls are 8 feet tall.

What is the surface area of the walls and ceiling to be painted? Ignore any doors or windows.

Answers

Answer:

Step-by-step explanation:

ceiling 22² = 484 ft²

walls 4(22)(8) = 704 ft²

Total  1188 ft²

đối với hai bài toán ước lượng cho u p

Answers

Chuong2: ƯỚC LƯỢNG THAM SỐ, môn thống kê ứng dụng

What is an equation of the line that passes through the point (4, −1) and has
slope −5?

Answers

Answer:

y + 1 = -5(x - 4)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate y₁ - y coordinate m - slope

Step-by-step explanation:

Step 1: Define

Identify variables.

Point (4, -1) → x₁ = 4, y₁ = -1

Slope m = -5

Step 2: Find Equation

Substitute in variables [Point-Slope Form]:                                                    y - -1 = -5(x - 4)Simplify:                                                                                                             y + 1 = -5(x - 4)

what do I do next???​

Answers

Answer: You have to get rid of the variables (the x's) so subtract 2x from 2x and 11x then go from there.

Step-by-step explanation:

Answer:

3 and 6

Step-by-step explanation:

11x - 53 = x^2 + 2x - 35

Subtract 11x - 53 on both sides,

0 = x^2 + 2x - 35 - ( 11x - 53 )

  = x^2 + 2x - 35 - 11x + 53

  = x^2 + 2x - 11x + 53 - 35

0 = x^2 - 9x + 18

x^2 - 9x + 18 = 0

Now this equation need to factorized.

x^2 - 9x + 18 = 0

x^2 - 3x - 6x + 18 = 0

x ( x - 3 ) - 6 ( x - 3 ) = 0

( x - 3 ) ( x - 6 ) = 0

x - 3 = 0

x = 3

x - 6 = 0

x = 6

The solutions to this system are 3 and 6.

A hiker starts at an elevation of 12 feet above sea level. She descends 43 feet into an
underground cave to explore. While exploring, she slips and slides 17 feet further down
into the cave. Write an expression that can be used to model this situation and evaluate
it to determine her location below sea level.

Answers

Answer:

if its asking for final depth it is 48 fert below sea level

Step-by-step explanation:

43 + 17= 60

12 - 60 = 48

Use a table to find the solution to the situation.
Stan needs a mime. Mime A is offering his services for an initial $150 in addition to $25 per hour. Mime B
is offering her services for an initial $45 in addition to $40 per hour. When will the two mimes charge the
same amount of money?
The two mimes will charge the same amount of money after
hours.

Answers

Answer:

The answer is 3 hours

Step-by-step explanation:

Elias is making copies of a business meeting agenda. He needs one copy per person. If there are 3 representatives from each department attending, and there are 9 departments total, how many copies does he need to make?

Answers

Answer:

27 copies

Step-by-step explanation: since there are 3 representatives for each department and there are 9 then you multiply 9 and 3 to get your answer.

what is 7/9÷1/3 plz help thanks​

Answers

Answer:

[tex]2\frac{1}{3}[/tex]

Step-by-step explanation:

Alrighty, when dividing fractions there is a trick called "keep, change, flip".

Step 1: Keep- Keep the first fraction the same

[tex]\frac{7}{9}[/tex]

Step 2: Change- Change the division sign to a multiplication sign

[tex]\frac{7}{9} *[/tex]

Step 3: Flip- Flip the second fraction (the reciprocal)

[tex]\frac{1}{3} --->\frac{3}{1}[/tex]              [tex]\frac{7}{9} * \frac{3}{1}[/tex]

Then, you multiply straight across

[tex]\frac{7}{9} * \frac{3}{1} = \frac{21}{9}[/tex]

Now, we simplify

[tex]\frac{21}{9} = \frac{7}{3} = 2\frac{1}{3}[/tex]

3(x-4)-(2x+8) simplify

Answers

Answer:

x-20

Step-by-step explanation:

check a math app if u want to see

Heeeeelllllllppppppp

Answers

1.

[tex]y=\frac{5}{3} x-2[/tex]

2.

[tex]y=-2x+2[/tex]

3.

[tex]y=x+5[/tex]

4.

[tex]y=\frac{1}{4}x[/tex]

Express 4/20 as a percentage.​

Answers

Answer:

20%

Step-by-step explanation:

Express 4/20 as a percentage.​

4/20 = 1/5

100 * 1/5 = 20%

Answer:

20%

Step-by-step explanation:

Hey there,

[tex]\frac{4*5}{20*5}[/tex]

[tex]\frac{20}{100}[/tex]

= 20%

Hope this helps you.

Let me know if you have any other questions :-)

help me with this calculation
(X-1).(1-x)

Answers

[tex](x-1) (1-x)\\\\=(x-1)(-1)(x-1)\\\\=-(x-1)^2\\\\=-(x^2- 2x +1)\\\\=-x^2+2x-1[/tex]

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