-3 (1/-3)=1 What property is this?^

A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed

Natali [406]

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

4 0

3 years ago

What is the y-coordinate of the red point ? A. -3 B. 2 C. -2 D. 3

scoundrel [369]

The correct answer is B. 2

3 0

3 years ago

Read 2 more answers

Naomi asked several classmates how much cash they had in their pocket. She recorded the data below:

AfilCa [17]

Answer:

the answer is $2,883$

Step-by-step explanation:

8 0

3 years ago

If sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............

svp [43]

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions.

<h3>How to simplify an expression by trigonometric expressions</h3>

Trigonometric expressions are formulas that utilize trigonometric functions. Trigonometric functions are a kind of trascendental functions, that is, functions that cannot be described in algebraic terms.

In this question we must simplify a given expression by using the following trigonometric formula:

sin 2x = 2 · cos x · cos x (1)

Now we proceed to expand the expression given:

x = sin 32

x = 2 · sin 16 · cos 16

x = 4 · sin 8 · cos 8 · cos 16

x = 8 · sin 4 · cos 4 · cos 8 · cos 16

Thus,

sin 4 · cos 4 · cos 8 · cos 16 = x/8

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions. $\blacksquare$

To learn more on trigonometric functions, we kindly invite to check this verified question: brainly.com/question/6904750

6 0

2 years ago

Consider the given function.

Misha Larkins [42]

Answer:

x -intercepts are x = -3 and x = 1

y-intercept at y = -3

The line of symmetry is x = -1

vertex is (h,k) = (-1,-4)

Step-by-step explanation:

Given a quadratic equations: h(x) = (x + 1)^2 - 4

The vertex for is :

h(x) = a(x - h)² + k

where,'h' is the axis of symmetry and (h,k) is the vertex.

So from the given equation we will rewrite the equation as:

h(x) = (x - (-1))^2 - 4

Hence,h = -1 and k = -4

The line of symmetry is x = -1 and vertex is (h,k) = (-1,-4)

Now, we have to find the x intercepts,

using the equation,

(x + 1)² = 4

Taking the square root on both sides,

√(x + 1)² = √4

x + 1 = ± 2

x = 1 or x = -3

So x -intercepts are x = -3 and x = 1

For y-intercept put x = 0 into the real equation:

h(x) = (0 +1)^2 - 4

y = 1 - 4

y = -3

So y-intercept at y = -3

Here with I have attached the graph.

Thank you.

5 0

3 years ago

Read 2 more answers

-3 (1/-3)=1 What property is this?^​

-3 (1/-3)=1 What property is this?^