1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Radda [10]
3 years ago
8

The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba

sed on the region of the country the warehouse is located. She randomly selects 35 employees who work in warehouses on the East Coast (Group 1) and 35 employees who work in warehouses in the Midwest (Group 2) and records the number of parts shipped out from each for a week.
She finds that East Coast group ships an average of 1276 parts and knows the population standard deviation to be 347.
The Midwest group ships an average of 1439 parts and knows the population standard deviation to be 298.
Using a 0.01 level of significance, test if there is a difference in productivity level. What is the test statistic?
(Round to 4 decimal places)
z =
please use excel to solve
Mathematics
1 answer:
blsea [12.9K]3 years ago
7 0

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

H_0: \mu_1 - \mu_2 = 0

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

H_1: \mu_1 - \mu_2 \neq 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = \mu_1 - \mu_2 = 1276 - 1439 = -163

s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144

Test statistic:

z = \frac{X - \mu}{s}

z = \frac{-163 - 0}{77.3144}

z = -2.11

The test statistic is z = -2.11.

You might be interested in
-11 2/3 × ( -4 1/5 )=​
galina1969 [7]
The answer is 49
Solving Steps

8 0
2 years ago
How many lines of symmetry does the shape have?
jenyasd209 [6]
12
The shape has 12 lines of symmetry because you add
up all the sides
6 0
3 years ago
Which of the following is a solution of x^2+8x= -32
juin [17]

Answer:

X1=-4+4i

X2=-4-4i

Step-by-step explanation:

X^2+8x+32=0

Δ=b^2-4ac=8^2-4(32)=-64<0

X1=(-b-i√Δ) /2a=(-8-8i)/2=-4-4i

X2=(-b+i√Δ) /2a=(-8+8i)/2=-4+4i

3 0
2 years ago
Can I get your opinion on if this looks right and if not, how should it be done?
mrs_skeptik [129]
It looks good to me!!
3 0
3 years ago
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent
vazorg [7]

Answer:

Step-by-step explanation:

cos(34) =sin(56)

cos(77)=sin(13)

sin(25)=cos(65)

sin(61)=cos(29)

7 0
2 years ago
Other questions:
  • For the given functions f (x), let x0 = 0, x1 = 0.6, and x2 = 0.9. construct interpolation polynomials of degree at most one and
    10·1 answer
  • What is ​ 7/25 ​ written as a decimal?
    14·2 answers
  • Continuity M8 Orade &amp; PreAlgebra Qun 4 (8V10-20) UPDATED
    10·1 answer
  • A bag contains 6 red tiles, 8 blue tiles, and 6 green tiles. A tile is drawn, the color recorded, and then the tile placed back
    5·1 answer
  • S=a+b+c <br> solve for b<br> Completely forgot how to do this
    13·1 answer
  • Use the reciprocal property to solve for x : 3/540= 10/x
    13·1 answer
  • What is the solution to the system of equations?
    9·2 answers
  • Need help asap !!!!!!!
    13·2 answers
  • Shara has a garden that has a perimeter of 14 feet and a length of 4 feet. What is the width?
    7·1 answer
  • Hey could you guys help me answer this and explain it to me? It’s math
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!