Help on this plsssss

A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quar

kotykmax [81]

Answer:

a

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

b

The 95% confidence interval is $0.224 < \mu_1 - \mu_2 < 2.776$

Step-by-step explanation:

From the question we are told that

The sample size is n = 36

The first sample mean is $\= x_1 = 11.4$

The first standard deviation is $s_1 = 2.5$

The second sample mean is $\= x_2 = 9.9$

The second standard deviation is $s_2 = 3.0$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 0$

Generally the test statistics is mathematically represented as

$z = \frac{ (\= x_1 - \= x_2 ) - (\mu_1 - \mu_2 ) }{ \sqrt{ \frac{s_1^2 }{n} + \frac{s_2^2 }{ n} } }$

=> $z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }$

=> $z = 2.3$

From the z table the area under the normal curve to the left corresponding to 2.3 is

$P( Z > 2.3 ) = 0.010724$

Generally the p-value is mathematically represented as

$p-value = 2 * P( Z > 2.3 )$

=> $p-value = 2 * 0.010724$

=> $p-value = 0.02$

From the value obtained we see that $p-value < \alpha$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

Considering question b

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{s_1^2 }{n } + \frac{s_2^2}{n}}$

=> $E = 1.96 * \sqrt{ \frac{2.5^2 }{ 36 } + \frac{ 3^2}{36}}$

=> $E = 1.276$

Generally 95% confidence interval is mathematically represented as

$( \= x_1 - \= x_2) -E < \mu_1 - \mu_2 < ( \= x_1 - \= x_2) + E$

=> $( 11.4 - 9.9 ) -1.276 < \mu_1 - \mu_2 < ( 11.4 - 9.9 ) + 1.276$

=> $0.224 < \mu_1 - \mu_2 < 2.776$

4 0

3 years ago

the interest paid for borrowing qn amount of money for 3yrs at the rate of 4%is n108 find the amount of the money borrowed

tankabanditka [31]

Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x where r is the growth rate (interest rate)

So the equation can be written as

$m= P(1.04)^t$ where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

$I = P(1.04)^t-P$ where I represents the interest paid.

plug the values into the equation

$108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P$

3 0

2 years ago

Categorize the graph as linear increasing, linear decreasing, exponential

photoshop1234 [79]

Linear decreasing because it is a line with a negative slope

3 0

4 years ago

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PLEASE HELP ME I WILL CHOOSE BRAINLIEST!!!!

kakasveta [241]

Answer:

Exact height = 8*sqrt(3) mm

Approximate height = 13.856 mm

=============================================================

Explanation:

If you do a vertical cross section of the cylinder, then the 3D shape will flatten into a rectangle as shown in the diagram below.

After flattening the picture, I've added the points A through F

point A is the center of the sphere and cylinder
points B through E are the corner points where the cylinder touches the sphere
point F is at the same horizontal level as point A, and it's on the edge of the cylinder.

Those point labels will help solve the problem. We're told that the radius of the sphere is 8 mm. So that means segment AD = 8 mm.

Also, we know that FA = 4 mm because this is the radius of the cylinder.

Focus on triangle AFD. We need to find the height x (aka segment FD) of this triangle so we can then double it later to find the height of the cylinder. This in turn will determine the height of the bead.

------------------------------

As the hint suggests, we'll use the pythagorean theorem

a^2 + b^2 = c^2

b = sqrt(c^2 - a^2)

x = sqrt(8^2 - 4^2)

x = sqrt(48)

x = sqrt(16*3)

x = sqrt(16)*sqrt(3)

x = 4*sqrt(3)

This is the distance from D to F

The distance from D to E is twice that value, so DE = 2*(FD) = 2*4*sqrt(3) = 8*sqrt(3) is the exact height of the bead (since it's the exact height of the cylinder).

Side note: 8*sqrt(3) = 13.856 approximately.

8 0

3 years ago

-7.5÷4.25 Awnser: Explain:

Lana71 [14]

Answer:

the answer is 1.76 I believe

7 0

3 years ago

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