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
Anika [276]
3 years ago
9

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such tha

t it would produce a mean pressure of 6.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.3 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Mathematics
2 answers:
alekssr [168]3 years ago
7 0

Answer:

t=\frac{6.3-6.0}{\frac{1}{\sqrt{26}}}=1.530  

df = n-1 = 26-1=25

Since is a right-sided test the p value would be:  

p_v =P(t_{25}>1.530)=0.0693  

If we compare the p value and the significance level given \alpha=0.025 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is significantly higher than 6.0

Step-by-step explanation:

Data given and notation  

\bar X=6.3 represent the sample mean    

s=1.0 represent the sample standard deviation

n=26 sample size  

\mu_o =6.0 represent the value that we want to test  

\alpha=0.025 represent the significance level for the hypothesis test.  

z 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 the ture mena is higher than 6.0, the system of hypothesis would be:  

Null hypothesis:\mu \leq 6.0  

Alternative hypothesis:\mu > 6.0  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

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

t=\frac{6.3-6.0}{\frac{1}{\sqrt{26}}}=1.530  

P-value  

The degrees of freedom are given by:

df = n-1 = 26-1=25

Since is a right-sided test the p value would be:  

p_v =P(t_{25}>1.530)=0.0693  

Conclusion  

If we compare the p value and the significance level given \alpha=0.025 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is significantly higher than 6.0

-Dominant- [34]3 years ago
3 0

Answer:

The null hypothesis failed to be rejected.

There is no enough evidence to support the claim that the valve performs above the specifications.

Step-by-step explanation:

The claim is that the valve performs above the specifications. That is that the valve produce a mean pressure higher than 6.0.

Then, the null and alternative hypothesis are:

H_0: \mu=6.0\\\\H_a:\mu>6.0

The significance level is 0.025.

We have a sample of size n=26, in which the sample mean is 6.3 and the standard deviation is 1.0.

As the standard deviation of the population is estimated from the sample, a t-test will be performed.

The degrees of freedom are:

df=n-1=26-1=25

The t-statistic is:

t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{6.3-6.0}{1.0/\sqrt{26}}=\dfrac{0.3}{0.196}=1.53

The p-value for this right tailed test and 25 degrees of freedom is:

P-value=P(t>1.53)=0.0693

The P-value is greater than the significance level, so the effect is not significant. The null hypothesis failed to be rejected.

There is no enough evidence to support the claim that the valve performs above the specifications.

You might be interested in
Find the distance between the two points in simplest radical form. (4, 4) { and } (8, -3)
Temka [501]

Answer:

привет, я не знаю, как ответить на вопрос

Step-by-step explanation:

5 0
2 years ago
NEED HELP NOW PLEASE HELP
NemiM [27]

Answer:

The answer is 1,980

Step-by-step explanation:

660*3= 1980

3 0
2 years ago
Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 5; B: the numbers add to 2
labwork [276]

Answer:

Part 1

A = {5}

B = {(1,1)}

C = {(2,1), (2,3), (2,4), (2,5), (2,6), (1,2), (3,2), (4,2), (5,2), (6,2)}

D =  {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,6), (4,1), (4,2), (4,3), (4,5), (4,6), (5,1), (5,2), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

Part 2

35

Step-by-step explanation:

Part 1

We use brakets for indicate that the elements belong to a event.

In each event, the first member of each parentheses belong to dice red and the second belong to green dice.

We consider in each event all elements that accomplish the condition.

Part 2

When we combinate pair with the two dice obtain 36 pairs (6*6, six possible results in the red dice and six possible results in the green dice), now we look for all of them that do not add 2.

(1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

4 0
3 years ago
The total cost (c) in dollars of renting a car for n days is given by the inequality LaTeX: c\ge125+50nc ≥ 125 + 50 n. What is t
zysi [14]

Answer:

<h3>6 days</h3>

Step-by-step explanation:

Given the inequality expression of the total cost (c) in dollars of renting a car for n days as c ≥ 125 + 50n

To get the maximum number of days for which a car could be rented if the total cost was $425, substitute c = 425 into the expression and find n

425 ≥ 125 + 50n

Subtract 125 from both sides

425 - 125 ≥ 125 + 50n  - 125

300≥ 50n

Divide both sides by 50

300/50≥50n/50

6 ≥n

Rearrange

n≤6

<em>Hence the maximum number of days for which a car could be rented if the total cost was $425 is 6days</em>

<em></em>

5 0
3 years ago
Please help me???????
Troyanec [42]
Part 1
1. 16-composite
2. 0- Neither
3. 29- prime
4. 33- composite
5. 47- prime
6. 51- composite
7. 64- Composite
8. 73- prime
9. 12- Composite
10. 24- Composite
11. 17- prime
12. 38- composite
7 0
3 years ago
Other questions:
  • A triangle has an area of 1102 m², and two of the sides of the triangle have lengths 60 m and 56 m. find the angle included by t
    8·1 answer
  • Simplify
    14·1 answer
  • In the circle above, the length of AO is 1, and x = 88º. What is the area of sector AOB?
    10·2 answers
  • Donner Summit, California, is a popular ski resort area. Over the past 60 years, the annual snowfall totals of Donner Summit hav
    11·2 answers
  • What is the common difference d of the sequence? -15, -4, 7, 18, 29
    6·1 answer
  • In 1992, 18.6% of the world population was undernourished. In 2015, 10.9% of the population was undernourished. The average perc
    10·1 answer
  • Evaluate 4m-10-8=-2+12
    9·2 answers
  • Please help me .....
    9·1 answer
  • State weather (-2)3 will be positive or negative
    11·1 answer
  • Please someone help me with this question
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!