Mathematics, 04.12.2019 04:31 payshencec21

An engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100100 engines and the mean pressure was 7.27.2 lbs/square inch. assume the variance is known to be 0.810.81. if the valve was designed to produce a mean pressure of 7.37.3 lbs/square inch, is there sufficient evidence at the 0.010.01 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.

Answers: 3

Show answers

Answers

Answer from: tiggyandrep2dbee

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

p_v =P(z

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=7.2$ represent the sample mean

$\sigma=0.81$ represent the population standard deviation

n=100 sample size

$\mu_o =7.3$ represent the value that we want to test

$\alpha=0.01$ 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)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

3) Calculate the statistic

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

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

4) P-value

Since is a one-side lower test the p value would given by:

p_v =P(z

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

Answer from: Quest

There is no graph to go along with this

Answer from: Quest

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 13:50

James wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would james need to keep the website for site a to be a better choice than site b? 1. define a variable for the situation. 2. write an inequality that represents the situation. 3.solve the inequality to find out how many months he needs to keep the website for site a to be less expensive than site b. 4. using words, describe how many months he needs to keep the website for site a to be less expensive than site b.

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

If f(x) = 4x – 3 and g(x) = 8x + 2, find each function value a.f[g(3)] b.g[f(5)] c.g{f[g(-4)]}

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

The wheels of a bicycle have a diameter of 70cm. how many meters will the bicycle travel if each wheel makes 50 revolutions

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

How are sas and sss used to show that two triangles are congruent?