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
Sergio [31]
3 years ago
10

When working properly, a machine that is used to makes chips for calculators does not produce more than 4% defective chips. When

ever the machine produces more than 4% defective chips, it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes samples of chips and inspects them to determine if they are good or defective. One such random sample of 200 chips taken recently from the production line contained 12 defective chips. Find the p-value to test the hypothesis whether or not the machine needs an adjustment. What would your conclusion be if the significance level is 2.5%
Mathematics
1 answer:
Anika [276]3 years ago
8 0

Answer:

The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

Step-by-step explanation:

In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.

The hypothesis can be defined as follows:

<em>H</em>₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. <em>p</em> ≤ 0.04.

<em>H</em>ₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. <em>p</em> > 0.04.

The information provided is:

<em>X</em> = 12

<em>n</em> = 200

<em>α</em> = 0.025

The sample proportion of defective chips is:

\hat p=\frac{X}{n}\\\\=\frac{12}{200}\\\\=0.06

Compute the test statistic as follows:

z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\=\frac{0.06-0.04}{\sqrt{\frac{0.04(1-0.04)}{200}}}\\\\=1.44

The test statistic value is 1.44.

Decision rule:

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

Compute the <em>p</em>-value of the test:

p-value=P(Z>1.44)\\=1-P(Z

The <em>p</em>-value of the test is 0.075.

<em>p</em>-value = 0.075 > <em>α</em> = 0.025

The null hypothesis was failed to be rejected at 2.5% level of significance.

Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.

You might be interested in
Simplify: -14cd-2c^2d^2+15cd+9c^2d^2-15cd
MaRussiya [10]

7c^2d^2-14cd

Hope this helps a bunch!!!!!!!!!!!!

7 0
3 years ago
Evaluate √16-x when x=8.
PIT_PIT [208]
D
Sq rt of 8 is sq rt of 4 times sq rt of 2
3 0
3 years ago
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown. What is the function written in vertex form?
pychu [463]
F(x) = 5(x + 4) – 80
f(x) = 5(x + 8) – 80
f(x) = 5(x + 4)2 – 80
f(x) = 5(x + 8)2 – 80
4 0
3 years ago
Which graph represents the given equation? <br><br> Y = 3/2x^2 + 4x - 2
lana [24]

Answer:

The graph is B

8 0
3 years ago
The length of a rectangle is 3 times the width.If the length is decreased by 4 m and the width is increased by 1 m , the perimet
o-na [289]

Answer:

Length = 27 metres

Width = 9 metres

Step-by-step explanation:

Consider the width to be x.

Then the length will be 3x.

The perimeter is 66m when the width is increased by 1m and the length is decreased by 4m.

So the dimensions will become:

Length=3x-4

Width=x+1

Now solve for the variable x using the formula for perimeter of a rectangle:

P = 2(l+b)

66 = 2(3x-4+x+1)     (Divide both sides by 2 and simplify the parentheses)

33 = 4x-3      (Add 3 to both sides)

36 = 4x        (Divide both sides by 4)

x = 9

Now plug-in the value of x into the original dimensions which were:

Length=3x

Width=x

So the dimensions are:

Length = 27 metres

Width = 9 metres

6 0
3 years ago
Other questions:
  • suppose that you decide to spend no more than $30 for tickets. What are the possible combinations of small and large rides that
    11·2 answers
  • 35 points!!! will give Brainliest!!!! Hurry help please!!!
    14·1 answer
  • 14 students in neils class play basketball. 35 percent of the students in his class play basketball. How many total students are
    14·2 answers
  • A tennis racket normally costs ​$80. The tennis racket is on sale for 40​% off. What is the sale price of the tennis​ racket?
    9·2 answers
  • 1. Name the x- and y-intercepts for the equation: 2x + y = 6 (0, 3) and (60) (0, -3) and (-6,0) (3,0) and (0,6) (-3,0) and (0, -
    10·2 answers
  • How to solve thus through substitution method. please do it step by step
    11·2 answers
  • Find the area of a regular
    9·2 answers
  • If ∠2 = 82°, then ∠7= ?<br> look at image
    8·2 answers
  • Pls answer :c ! I need help ASAP ! (Math)
    8·1 answer
  • 40 POINTS <br><br> please answer me this question with an explanation
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!