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
Solve this equation:<br><br> |x-2|=6x+18
sineoko [7]
X-2=6x+18
-x -x
-2=5x+18
-18 -18
-20=5x
x=-4
5 0
2 years ago
Round$6.3572 to the nearest cent
Oxana [17]

$6.36

you have two digits in the cents place, so your third decimal would be the factor that rounds up or down, since the number is above 5 you round up

8 0
3 years ago
Read 2 more answers
What is the surface area of the cylinder?
Murrr4er [49]
The answer is B. 128.1
7 0
2 years ago
How can 8 ounces be expressed in pounds
vichka [17]

The answer would be .5 pounds

1 ounce is equal to .0625 lbs

so 8 * .0625 = .5

hope this helps :)

brainliest???

4 0
3 years ago
Read 2 more answers
Please don't put links:(​
GalinKa [24]

1/2 brainlest please

Step-by-step explanation:

It would be 0 then 1/2 then 2/2 then finally 1

7 0
2 years ago
Other questions:
  • ¿CUAL ES EL PERIMETRO DE UN RECTANGULO SABIENDO QUE SU ANCHO ES 3/4 DEL LARGO Y BEL LARGO MIDE 2,55M?
    11·1 answer
  • 75 cents/h= dollars/days
    13·2 answers
  • PLEASE help and explain hoot do this. I need help with 4,5,6
    15·1 answer
  • After 56 cans of soup were sold, a clerk moved the remaining cans to a display
    9·1 answer
  • 7n - 4 = 31
    11·1 answer
  • Write 171 in 3 as a unit rate
    5·1 answer
  • Helpppppppppppppppppppppp
    15·1 answer
  • If the mean of a given dataset is 131 and the standard deviation is 8, where will a majority of the data lie?
    6·2 answers
  • Which system of equations is represented by the graph?
    7·2 answers
  • If y=kx, where k is a constant, and y=24 when x=6, what is the value of y when x=5?A. 6B. 15C. 20D. 23
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!