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
coldgirl [10]
3 years ago
14

A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed

of the film, and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film the sample data result is x1 = 1.17 and s1 = 0.11 , while for the 20-mil film, the data yield x2 = 1.04 and s2 = 0.09 . Note that an increase in film speed would lower the value of the observation in microjoules per square inch.
Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use alpha=0.05
Mathematics
1 answer:
Natali [406]3 years ago
4 0

Answer:

t=\frac{1.17-1.04}{\sqrt{\frac{0.11^2}{8}+\frac{0.09^2}{8}}}}=2.587  

df=n_{1}+n_{2}-2=8+8-2=14

Since is a one sided test the p value would be:

p_v =P(t_{(14)}>2.587)=0.0108

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, we have enough evidence to reject the null hypothesis on this case and the 25 mil film have a mean greater than the 20 mil film so then the claim is not appropiate

Step-by-step explanation:

Data given and notation

\bar X_{1}=1.17 represent the mean for the sample 1 (25 mil film)

\bar X_{2}=1.04 represent the mean for the sample 2 (20 mil film)

s_{1}=0.11 represent the sample standard deviation for the sample 1

s_{2}=0.09 represent the sample standard deviation for the sample 2

n_{1}=8 sample size selected for 1

n_{2}=8 sample size selected for 2

\alpha=0.05 represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if reducing the film thickness increases the mean speed of the film, the system of hypothesis would be:

Null hypothesis:\mu_{1} \leq \mu_{2}

Alternative hypothesis:\mu_{1} > \mu_{2}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

t=\frac{1.17-1.04}{\sqrt{\frac{0.11^2}{8}+\frac{0.09^2}{8}}}}=2.587  

P-value

The first step is calculate the degrees of freedom, on this case:

df=n_{1}+n_{2}-2=8+8-2=14

Since is a one sided test the p value would be:

p_v =P(t_{(14)}>2.587)=0.0108

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, we have enough evidence to reject the null hypothesis on this case and the 25 mil film have a mean greater than the 20 mil film so then the claim is not appropiate

You might be interested in
The surface area of the square pyramid is 96 square inches. Find the value of x.
anyanavicka [17]

Answer:

X is 24.

Step-by-step explanation:

Divide the surface area by 4

5 0
3 years ago
Read 2 more answers
Is 4/6 more less or equal to half
olasank [31]

Answer:

more

Step-by-step explanation:

4/6 simplified is 2/3

3/6 would be half

7 0
3 years ago
In a certain county, the number of Charter Schools is eleven less than twice the number of Alternative Schools. There are 35 Cha
vitfil [10]
Id have to say 2a-11=35 

5 0
3 years ago
Claudia is on a motorcycle trip. She checked the odometer at the beginning of the trip, and it showed 16,789 miles. After 15 day
11Alexandr11 [23.1K]
22,189 - 16,789 = 5400....so she drove/rode 5400 miles in 15 days

5400/15 = 360 miles per day <==
5 0
3 years ago
PLEASEEEEE HELPPPPP!!!!
Dmitry_Shevchenko [17]

Step One

Find AM

Formula

AM = MN - AN

Givens

MN = 67.2

AN = 32

Solution

AM - 67,2 - 32

AM = 35.2

Step Two

Set up a solution

67.2/35.2 = 81.9/x            Cross Muliply

67.2 * x   =    81.9 * 35.2   Combine the right

67.2 * x = 2882.88            Divide by 67.2

x = 2882.88/67.2

x = 42.9                             Answer

3 0
3 years ago
Other questions:
  • Ali picked 3 numbers out of a hat.
    12·2 answers
  • Select the function that whose end behavior is described by
    11·2 answers
  • Lin says she can map Polygon A to Polygon B using only reflections. Do you agree with Lin ? Explain your reasoning
    14·1 answer
  • Using appropriate properties find
    5·1 answer
  • There are only blue yellow and green cubes in a bag
    12·1 answer
  • A stereo speaker in the shape of a triangular pyramid has a height of 8.25 inches. The area of the base of the speaker is 22 squ
    6·1 answer
  • Solve the equation for all values of x.<br> (x2 – 16)(x2 + 49) = 0
    13·1 answer
  • What is the answer to this problem if you need to find out the area?
    11·1 answer
  • Emergency please help I have been trying to solve this all day I am stûpid
    9·1 answer
  • What is the slope??<br> (The bottom one says : (-6, -5)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!