Mathematics, 27.02.2020 18:29 ft2134

The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens is selected, and the average tensile strength is found to be 127 psi.
(a) Test the hypothesis that the mean tensile strength equals 125 psi versus the alternative that the mean exceeds 25 psi. Use ? = 0.05.
(c) Discuss why a one-sided alternative was chosen in part (a).

Answers: 3

Show answers

Answers

Answer from: Jasten

a) $z=\frac{127-125}{\frac{2}{\sqrt{8}}}=2.828$

Since is a one-side upper test the p value would be:

p_v =P(z2.828)=1-P(z

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 reject the null hypothesis, and we can conclude that the true mean is higher than 125

b) We select a one sided interval since the interest is in analyze if the true mean is higher than 125, and then the alternative hypothesis needs to be the alternative hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=127$ represent the mean for the sample

$\sigma=2$ represent the standard deviation for the population

n=8 sample size

$\mu_o =125$ represent the value that we want to test

$\alpha$ 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)

Part a

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the true mean is higher than 125:

Null hypothesis: $\mu = 125$

Alternative hypothesis: $\mu 125$

We know the population deviation, so for this case 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".

Calculate the statistic

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

$z=\frac{127-125}{\frac{2}{\sqrt{8}}}=2.828$

Calculate the P-value

Since is a one-side upper test the p value would be:

p_v =P(z2.828)=1-P(z

Conclusion

Part b

We select a one sided interval since the interest is in analyze if the true mean is higher than 125, and then the alternative hypothesis needs to be the alternative hypothesis.

Answer from: Quest

afjnawenkfnjaw; enkanwelwaklalejjaw; fij

step-by-step explanation:

Answer from: Quest

Def is a scalene triangle

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Which is the completely factored from of xy^3-x^3y

Answers: 3

Answer

Mathematics, 21.06.2019 17:00

According to modern science, earth is about 4.5 billion years old and written human history extends back about 10,000 years. suppose the entire history of earth is represented with a 10-meter-long timeline, with the birth of earth on one end and today at the other end.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Find the zeros of each function. f(x) = 6x^2 - 7x - 20

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

If 30 lb of rice and 30 lb of potatoes cost ? $27.60? , and 20 lb of rice and 12 lb of potatoes cost ? $15.04? , how much will 10 lb of rice and 50 lb of potatoes? cost?

Answers: 1

Answer

You know the right answer?

The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previou...

Questions