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
Can someone help me with this question
Contact [7]

well, since each bar is parallel to the adjacent one, so if A || B || C || D || E || F, then A || F.

now, for the angles, Check the picture below.

6 0
2 years ago
Andre received $60 for his birthday and put it in his piggy bank. Each week, he put 3 more dollars in the bank. The amount of mo
Dahasolnce [82]

Answer:

96 (dollars)

Step-by-step explanation:

D represents the amount of money Andre has in his bank after w weeks.  This formula is written as D(w) = 3w + 60 (dollars).

After 12 weeks, Andre will have accumulated D(12) = 3(12) + 60 dollars, or

36 + 60 dollars, or 96 dollars.  This is answer choice B.

3 0
3 years ago
I need help (;´༎ຶٹ༎ຶ`)
nasty-shy [4]
445 + 210 + 525 = 1,180

500 + 85x = 1,180
-500 -500

85x = 680
/85 /85

x = 8
3 0
3 years ago
You are deciding between two cell phone plans. Plan A: Unlimited text, talk, and data for $50 per month. Plan B: Unlimited text
Sergio039 [100]
Sent a picture of the solution to the problem (s).

7 0
3 years ago
-1/2÷ _____ = -7/3. what is the missing number
satela [25.4K]
3/14 i think.................
7 0
3 years ago
Other questions:
  • It should take 5.22 minutes to clean a shower. You have 5 showers that need to be cleaned. How many minutes should it take for y
    15·1 answer
  • Fill in the blank with a symbol that makes this statement true 5/12 and 1/3
    10·1 answer
  • Please I need your help. Answer the questions following the grammar rules.
    8·2 answers
  • How to describe a transformation?
    11·1 answer
  • Please help if you know how to use Similarity in Geometry! <3 *
    8·1 answer
  • 1. You and your friend mix water and citric acid. You add 3 cups of citric acid for every
    7·1 answer
  • Please help me thanks y’all
    13·2 answers
  • Each football player is recommended to drink a minimum of 540 milliliters of water for every 1 hour of play. Aaron expects to pl
    9·1 answer
  • Need help with a math problem
    13·2 answers
  • Plz help me with these 2 problems
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!