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
11Alexandr11 [23.1K]
2 years ago
9

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line. He must recalibrate his machines

if the bolts are too long or too short. After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm. He knows that the population standard deviation is 0.83 cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? State the null and alternative hypotheses for the test.
Mathematics
1 answer:
storchak [24]2 years ago
5 0

Answer:

The null hypothesis is H_o: \mu = 4.

The alternate hypothesis is H_a: \mu \neq 4

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

H_o: \mu = 4

At the alternate hypothesis we test if it is different. So

H_a: \mu \neq 4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that \mu = 4

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that n = 196, X = 4.14

He knows that the population standard deviation is 0.83 cm.

This means that \sigma = 0.83

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}

z = 2.36

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

You might be interested in
I NEED HELP PLS THIS IS DUE TOMORROW
Aleks [24]

Answer:

6x -10 = 5x+12 (vertically opposite angles)

6x-5x =12+10

x= 22

Step-by-step explanation:

Pls mark as brainliest

8 0
2 years ago
Read 2 more answers
A circle with center c(4,-2) contains the point D( 8,1). What is the equation of the line perpendicular to the radius of the cir
Nady [450]

Answer:

  4x +3y = 10

Step-by-step explanation:

The radius CD has slope Δy/Δx = (1-(-2))/(8-4) = 3/4.

The equation for the perpendicular line through point C(4, -2) can be written as ...

  Δx(x -4) +Δy(y -(-2)) = 0

  4(x -4) +3(y +2) = 0

  4x +3y -10 = 0 . . . . . . general form equation for the line

  4x +3y = 10 . . . . . . . . .standard form equation for the line

 

8 0
3 years ago
Figure 2 length 10 width find perimeter and area
Anestetic [448]
The answer to that question is four
4 0
2 years ago
Read 2 more answers
Write an equation that describes the function.
Leona [35]
From the points you get a slope of -1 using the slope in y=mx+b you get b=1 so y=-x+1
5 0
3 years ago
Read 2 more answers
Who can solve Multi-Step Literal Equations?: n/r=D/b
Nata [24]

Answer:

i/=-d:./k/-= sorry

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Identify the ordered pair that represents the vector from A(1,6) to B(2, -3) and the magnitude of AB-
    7·1 answer
  • A woman has 14 different shirts: 10 white shirts and 4 red shirts. If she randomly chooses 2 shirts to take with her on vacation
    12·1 answer
  • Kori spent $46.20 on 12 gallons of gasoline. What was the price per gallons
    13·2 answers
  • A long-distance runner runs 2 miles south and then 4 miles east. How far is the runner from the starting point?
    12·1 answer
  • Graph the exponential function g(x)=(3/5) ^x To graph the function plot the points on the graph with the x values -2 , -1,0,1 an
    13·1 answer
  • Karen and her sister Tina want to get a pet. However, Karen wants a turtle and Tina wants a dog. Their parents tell them to flip
    7·1 answer
  • A car’s value decreases 5% every year after it is purchased. If the original price of the car was $30,000, how much is the car w
    15·1 answer
  • Find the measure of arc x
    10·1 answer
  • If f(x) = 5 - 2x and g(x) = -4x + 2, find g(f(x))
    11·1 answer
  • 4 x 4/6 is it equal to, less than, or greater than
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!