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
5) In a urea manufacturing plan, all employees work a basic week of 40 hours. Ay overtime worked during weekdays is paid for at
Mkey [24]

Answer: $‭1,135.15‬

Step-by-step explanation:

First calculate his basic pay;

= 40 * 14.60

= $584

Total for overtime worked during the week;

= 15 * 14.60 * 1.25

= $‭273.75‬

Total for overtime worked on Saturday;

= 6 * 14.60 * 1.5

= $131.40

Total for overtime worked on Sunday;

= 5 * 14.60 * 2

= $146

Sum all the figures;

= 584 + 273.75 + 131.40 + 146

= $‭1,135.15‬

3 0
2 years ago
What is the value of the problem below?
Hitman42 [59]

Answer:

90

Step-by-step explanation:

The first term  = 6* 2^0 =  6

The second term = 6 * 2^ (2-1) = 6*2 = 12

The third term = 6* 2^(3-1) = 6*2^2 = 6*4 = 24

The fourth term = 6* 2^(4-1) = 6* 2^3 = 6*8 = 48

S4  is the sum of the 1st four terms

S4 = 6+ 12+24+ 48 = 90

7 0
3 years ago
Pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeee helpepppp meeeeeeeeeeeeeeeeeeeeeeee
Likurg_2 [28]
Answer : Option D





Step by step explanation :
There is a 50-50 chance of snowing in Hawaii.
4 0
2 years ago
Please help me with my math problem!!Thank you!! :)
vova2212 [387]

Check the picture below.

6 0
3 years ago
Aphrodite took out a 30-year loan from her bank for $170,000 at an APR of 7.2%, compounded monthly. If her bank charges a prepay
lora16 [44]
It's 3246.74 --- APEX
7 0
3 years ago
Other questions:
  • In a group of 60 children there are three times as many boys as girls.how many girls are there
    8·1 answer
  • How could you use multiplication to find 7+7+7?
    5·2 answers
  • Put a check by all the factors of 20.
    13·1 answer
  • Consider the points (−4, 0) and (5, 0).
    13·1 answer
  • The area of the base of a triangular pyramid with faces that are equilateral triangles is 64 ft squared. Can you find the surfac
    5·1 answer
  • pls help with this immediately!!!! i’ll be giving brainiest to those who provide the correct answer. if u leave a link, have fun
    13·2 answers
  • To rent a machine for 6 hours, it costs $27. How much will it cost to rent it<br> for 3 hours?
    7·1 answer
  • teds age is now four less than twice the age of his brother. The sum of their age is 50. what will be their ages three years fro
    11·1 answer
  • I very much need help, please. This is trigonometry.
    10·1 answer
  • A four-letter code uses the letters Z and X. Either letter can be repeated in the code. How many
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!