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
Nastasia [14]
3 years ago
6

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately

normally distributed and has a standard deviation of 20 mm. The company wishes to test H0: μ = 175 mm versus H1: μ > 175 mm, using a random sample of n = 10 samples.(a) Find P-value if the sample average is = 185? Round your final answer to 3 decimal places.(b) What is the probability of type II error if the true mean foam height is 200 mm and we assume that α = 0.05? Round your intermediate answer to 1 decimal place. Round the final answer to 4 decimal places.(c) What is the power of the test from part (b)? Round your final answer to 4 decimal places.
Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0

Answer:

a) 0.057

b) 0.5234

c) 0.4766

Step-by-step explanation:

a)

To find the p-value if the sample average is 185, we first compute the z-score associated to this value, we use the formula

z=\frac{\bar x-\mu}{\sigma/\sqrt N}

where

\bar x=mean\; of\;the \;sample

\mu=mean\; established\; in\; H_0

\sigma=standard \; deviation

N = size of the sample.

So,

z=\frac{185-175}{20/\sqrt {10}}=1.5811

\boxed {z=1.5811}

As the sample suggests that the real mean could be greater than the established in the null hypothesis, then we are interested in the area under the normal curve to the right of  1.5811 and this would be your p-value.

We compute the area of the normal curve for values to the right of  1.5811 either with a table or with a computer and find that this area is equal to 0.0569 = 0.057 rounded to 3 decimals.

So the p-value is  

\boxed {p=0.057}

b)

Since the z-score associated to an α value of 0.05 is 1.64 and the z-score of the alternative hypothesis is 1.5811 which is less than 1.64 (z critical), we cannot reject the null, so we are making a Type II error since 175 is not the true mean.

We can compute the probability of such an error following the next steps:

<u>Step 1 </u>

Compute \bar x_{critical}

1.64=z_{critical}=\frac{\bar x_{critical}-\mu_0}{\sigma/\sqrt{n}}

\frac{\bar x_{critical}-\mu_0}{\sigma/\sqrt{n}}=\frac{\bar x_{critical}-175}{6.3245}=1.64\Rightarrow \bar x_{critical}=185.3721

So <em>we would make a Type II error if our sample mean is less than 185.3721</em>.  

<u>Step 2</u>

Compute the probability that your sample mean is less than 185.3711  

P(\bar x < 185.3711)=P(z< \frac{185.3711-185}{6.3245})=P(z

So, <em>the probability of making a Type II error is 0.5234 = 52.34% </em>

c)

<em>The power of a hypothesis test is 1 minus the probability of a Type II error</em>. So, the power of the test is

1 - 0.5234 = 0.4766

You might be interested in
If the sum of a number and three is doubled?, the result is seven less than the number. Find the number
pentagon [3]
(x+3)*2=x-7
2x+6=x-7
x=-13
6 0
2 years ago
What the closest volume of a cylinder with a height of 10 and a circumference of 8
jenyasd209 [6]

In order to calculate the volume of a cylinder, we can use the following formula:

V=\pi r^2h

Where r is the base radius and h is the height.

If the circumference is 8, we have:

\begin{gathered} C=2\pi r \\ 8=2\pi r \\ r=\frac{4}{\pi} \end{gathered}

Now, calculating the volume, we have:

\begin{gathered} V=\pi(\frac{4}{\pi})^2\cdot10 \\ V=\frac{160}{\pi} \\ V=50.93 \end{gathered}

So the correct option is the second one.

3 0
1 year ago
4-(3-5)=<br> I need help
liraira [26]

Answer:

6

Step-by-step explanation:

I'm 99% sure you know the answer to this and didn't have to resort to this website.

3-5 = -2

Subtracting negative numbers means it becomes positive.

So the gist is that your adding 4 and 2 which is 6.

6 0
3 years ago
Which statement about the dilation of these triangles is true?
natulia [17]

Jabardasth question is the scale factor is 2

7 0
3 years ago
Read 2 more answers
Write the equation of the line that passes<br> through the points (-7,-9) and (-3,-1)
zysi [14]

Answer:

2x + 5

Step-by-step explanation:

I am assuming you are talking about a linear function. If it is, then the equation would be:

2x + 5.

Hope this helps!

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following are solutions?
    6·1 answer
  • Plz Help me with this question will give BRAINLIEST and 10 points!
    14·2 answers
  • How do you do this math problem
    15·1 answer
  • Carolines car used 16 gallons to travel 544 how far can she travel on 9 gallons
    9·2 answers
  • What is the measure of angle C?<br><br> A. 147°<br> B. 114<br> c. 33<br> D. 66
    14·2 answers
  • If the r-value, or correlation coefficient, of a data set is 0.934, what is the
    13·1 answer
  • HELP PLEASE
    15·1 answer
  • Three numerical expressions that are equivalent to (0.0004) x (0.005)
    8·1 answer
  • Can someone tell me what this is really quick
    14·1 answer
  • A right triangle with coordinates A (-1, 4), B(-1, 8) and C (3, 4) is first rotated 90 degrees counterclockwise and then transla
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!