Mathematics, 07.07.2020 20:01 sheltongraham1011

To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results. Type Sample Average Sample SD
1 60.7 1.0
2 60.5 1.0

Required:
a. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 100. (Round your answer to four decimal places.)
b. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 500. (Round your answer to four decimal places.)
c. Is the small P-value for n = 500 indicative of a difference that has practical significance

Answers: 3

Show answers

Answers

Answer from: sineguguhopengw3912

a. P-value = 0.1589

b. P-value = 0.0016

Step-by-step explanation:

a. This is a hypothesis test for the difference between populations means.

The claim is that the two types of steel have different true average fracture toughness values.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is α=0.05.

The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1. The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.

The difference between sample means is Md=0.2.

M_d=M_1-M_2=60.7-60.5=0.2

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142$

The degrees of freedom for this test are:

df=n_1+n_2-2=100+100-2=198

This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):

$P-value=2\cdot P(t1.4142)=0.1589$

As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

b. As the sample size changes, the standard error and the degress of freedom change.

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623$

The degrees of freedom for this test are:

df=n_1+n_2-2=500+500-2=998

This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):

$P-value=2\cdot P(t3.1623)=0.0016$

As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

Answer from: Quest

y= - $\frac{4}{3}$

Answer from: Quest

6/ 11 = 0.545454 so your answer is55%

Another question on Mathematics

Mathematics, 21.06.2019 13:20

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?

Answers: 2

Answer

Mathematics, 21.06.2019 17:30

What is the equation of a line passing through the point (6,1) and parallel to the line whose equation 3x=2y+4

Answers: 3

Answer

Mathematics, 21.06.2019 20:40

The graph of a function f(x)=(x+2)(x-4). which describes all of the values for which the graph is negative and increasing? all real values of x where x< -2 all real values of x where -2

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

What additional information is needed to prove that the triangles are congruent using the aas congruence theorem? o lolm o oama o zloa zlma o zlao – zlam

Answers: 1

Answer

You know the right answer?

To decide whether two different types of steel have the same true average fracture toughness values,...

Questions