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
Sedbober [7]
3 years ago
12

A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than

5% defective items, it needs repair. A random sample of 300 items taken from the production line contained 27 defective items. Test at the 1% significance level if the percentage of defective items produced by this machine is greater than 5%.
Mathematics
1 answer:
vovikov84 [41]3 years ago
5 0

Answer:

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

Step-by-step explanation:

A machine, when working properly, produces 5% or less defective items.

This means that the null hypothesis is:

H_0: p \leq 0.05

Test if the percentage of defective items produced by this machine is greater than 5%.

This means that the alternate hypothesis is:

H_a: p > 0.05

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.

0.05 is tested at the null hypothesis:

This means that \mu = 0.05, \sigma = \sqrt{0.05*0.95}

A random sample of 300 items taken from the production line contained 27 defective items.

This means that n = 300, X = \frac{27}{300} = 0.09

Value of the test statistic:

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

z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}

z = 3.18

Pvalue of the test:

Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.

Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993

1 - 0.9993 = 0.0007

The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.

You might be interested in
Slope -1/4, passes through (12,-4)​
Kazeer [188]

Answer:

y = - \frac{1}{4} x - 1

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - \frac{1}{4} , then

y = - \frac{1}{4} x + c ← is the partial equation

To find c substitute (12, - 4) into the partial equation

- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1

y = - \frac{1}{4} x - 1 ← equation of line

7 0
3 years ago
7/9 Z - 6/9 + 6 -5 / 9 Z - 9 simplify​
stepladder [879]

Answer:=2/9z+−11/3. the reason why this would answer is because you would have to combine like terms

8 0
3 years ago
Please help I am terrible at algebra
Marina CMI [18]

Answer:

y = (x-0)^2 + (-5)  ⇒ y = x^2 - 5

Step-by-step explanation:

The general vertex form of the parabola  y = a(x - h)² + k

Where (h,k) is the coordinates of the vertex.

As shown at the graph the vertex of the parabola is the point (0, -5)

So,

y = a(x-0) + (-5)

y = ax^2 - 5

To find substitute with another point from the graph like (1,-4)

So, at x = 1 ⇒ y = -4

-4 = a * 1^2 - 5

a = -4 + 5 = 1

<u>So, the equation of the given parabola is ⇒ y = x^2 - 5</u>

6 0
3 years ago
A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the
Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

25% of all adults had used the Internet for such a purpose

This means that \pi = 0.25

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

What is the required sample size for the new study?

This is n for which M = 0.03. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}

\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}

(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2

n = 800.3

Rounding up:

The required sample size for the new study is 801.

4 0
3 years ago
Label each of the triangles illustrated below
AVprozaik [17]
A: Equilateral
B: Obtuse
C: Obtuse
D: Right
E: Obtuse
F: Acute
8 0
3 years ago
Other questions:
  • 2(7g - 4h) - 6(5h - 3g)
    11·2 answers
  • Fill in the blank. ASAP . . . . .
    9·1 answer
  • Find the missing sides
    11·2 answers
  • Find the cartesian coordinates of the given polar coordinates. then plot the point. (a) (− 2 , 5π/4)
    8·1 answer
  • There are 40 girls and 32 boys who want to participate in 7th grade intramurals. If each team must have the same number of girls
    11·2 answers
  • Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
    7·1 answer
  • A gymnastics center charges a one -time membership fee of $35.75 . In addition , the center charges its members $55.50 per class
    10·1 answer
  • Which function is the inverse of f(x) = -5x-4?
    7·1 answer
  • -8x+4 less than or equal to 36
    14·2 answers
  • How many complex roots does the equation 0=3x5−x4−5x2+1 have?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!