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Katen [24]
3 years ago
6

Researchers would like to test if the mean bone mineral density is different for the three different groups. Conduct an ANOVA te

st to determine if there is a difference in the means of the 3 groups. Use a level of significance of LaTeX: \alpha = 0.05α = 0.05. What are the null and alternative hypotheses?
Mathematics
1 answer:
laiz [17]3 years ago
3 0

Answer:

<em>H</em>₀: <em>μ₁ = μ₂= μ₃</em>

<em>Hₐ: </em>At least one of the means is different.

Step-by-step explanation:

Analysis of variance or ANOVA test is used to determine whether the means of different groups are similar or not.

The hypothesis of an ANOVA test for <em>n</em> homogeneous groups is:

H_{0}: \mu_{1}= \mu_{2}= \mu_{3}...= \mu_{n}\\H_{a}: At\ least\ one\ of\ the\ means\ is\ different

In this case the researcher is testing whether the mean bone mineral density is different for the three different groups.

The hypothesis for this test can be defined as follows:

<em>H</em>₀: The mean bone mineral density is not different for the three different groups, i.e. <em>μ₁ = μ₂= μ₃</em>

<em>Hₐ: </em>The mean bone mineral density is different for the three different groups, i.e. at least one of the means is different.

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Answer:

a) P(X

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c) P(\bar X

And using a calculator, excel or the normal standard table we have that:

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d) Figure attached

e) If we don't know the distribution then we can't ensure that the sample mean would be distributed like this:

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And we can't estimate the probabilities on a easy way.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(2.5,0.03)  

Where \mu=2.5 and \sigma=0.03

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability on this way:

P(-0.50

Part b

Since the distribution for X is normal then the distribution for the sample mean is:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar X \sim N(2.5, \frac{0.03}{\sqrt{10}}=0.00948)

Part c

P(\bar X

And using a calculator, excel or the normal standard table we have that:

P(Z

Part d

See the figure attached the deviation for the sample mean is lower for this reason we have the pattern in the graph attached.

Part e

If we don't know the distribution then we can't ensure that the sample mean would be distributed like this:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we can't estimate the probabilities on a easy way.

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3 years ago
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The first option (-6 2/3, -2, 5/11, 7/8)

Step-by-step explanation:

This set of numbers is the only one that does not contain any positive numbers.

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3 years ago
An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelec
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Answer:

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Step-by-step explanation:

Given:

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The probability of getting a microprocessor from firm C is, P(C)=25\%=0.25

Now, let event D be having a defective microprocessor at random.

So, as per the question,

Probability of producing a defective microprocessor from firm A is, P(D/A)=6\%=0.06

Probability of producing a defective microprocessor from firm B is, P(D/B)=7\%=0.07

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Now, probability of having a defective microprocessor when selected at random is given as:

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Step-by-step explanation:

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