Mathematics, 23.07.2021 01:10 vcasela

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production method. If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? , , , , , , , , , , ,

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Answer from: ciel8809

To test a hypothesis, it means we want to verify or refute a claim. Here, we want to verify or refute whether the new method is better or not.

The new method is better, and the company should not take any action.

The given parameters are:

$\alpha = 0.05$ -- significance level

$\sigma =32.2$ -- the sample standard deviation

The missing data are:

x: -41,79,-22,-71,-42,13,18,53,-6,-50,-107,-107

n = 12

To solve this question, I will use the p-value method

The claim that the standard deviation is greater than 32.2 means that:

The alternate hypothesis is:

$H_a: \sigma 32.2$

The null hypothesis is:

$H_o: \sigma = 32.2$

So, we have:

$H_o: \sigma = 32.2$ --- null hypothesis

$H_a: \sigma 32.2$ --- alternate hypothesis

Start by calculate the mean value

$\bar x = \frac{\sum x}{n}$

$\bar x = \frac{-41+79-22-71-42+13+18+53-6-50-107-107}{12}$

$\bar x = \frac{-283}{12}$

$\bar x = -23.583$

Next, calculate the sample standard deviation

$\sigma_x =\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

This gives:

$\sigma_x =\sqrt{\frac{(-41--23.583)^2+(79--23.583)^2+.......+(-107--23.583)^2}{12-1}}$

$\sigma_x =\sqrt{\frac{37272.916668}{11}}$

$\sigma_x =\sqrt{3388.44696982}$

$\sigma_x =58.210368233$

Approximate

$\sigma_x =58.2$ --- to 1 decimal place

Next, calculate the test statistic using:

$t = \frac{(n - 1) * \sigma_x^2}{\sigma^2}$

$t = \frac{(12 - 1) * 58.2^2}{32.2^2}$

$t = \frac{11 * 58.2^2}{32.2^2}$

t = 35.94

Calculate the degrees of freedom (df)

df=n-1

df=12-1

df=11

So, we calculate the p-value with the following parameters

df=11

t = 35.94

The p value is

$p \approx 0$

Because the p value is less than the significance level

i.e. 0 < 0.05

We have to reject the null hypothesis and accept the alternative hypothesis

This means that the new method is better, and the company should not take any action.

Learn more about test of hypothesis at:

Answer from: Quest

2160ft^3 i think you could use a formala to you out with this in the future

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

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