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3 years ago

Is it possible for a simple, connected graph that has n vertices all of different degrees? Explain why or why not.

Mathematics

1 answer:

ryzh [129]3 years ago

8 0

Answer:

It isn't possible.

Step-by-step explanation:

Let G be a graph with n vertices. There are n possible degrees: 0,1,...,n-1.

Observe that a graph can not contain a vertice with degree n-1 and a vertice with degree 0 because if one of the vertices has degree n-1 means that this vertice is adjacent to all others vertices, then the other vertices has at least degree 1.

Then there are n vertices and n-1 possible degrees. By the pigeon principle there are two vertices that have the same degree.

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The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as b

Sonja [21]

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p > 0.3$

Right tailed test

b) $p_v =P(z>2.32)=0.0102$

c) So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p > 0.3$

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

For this case the statistic is given by $z_{calc}= 2.32$

Part b: Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.32)=0.0102$

Part c

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

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4 years ago

There are a total of 127 cars and trucks in a lot. If there are four more than twice the number of tricks than cars, how many ca

Kruka [31]

There are a total of 127 cars on a lot if there are four more than twice the number of trucks than cars how any trucks and cars are on the lot

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3 years ago

Price __________ works because human minds assign disproportionate weight to the first information they receive when making deci

Burka [1]

Answer:

Anchoring

Step-by-step explanation:

Price anchoring is when potential buying rely on first price information about the commodity to buy. Price anchoring is used to create a price reference point when making decision as compare to old price. It also gives customers perception of future price.

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3 years ago

What is the perimeter of a triangle with the given side lengths? s1 = x – 3 ft s2 = x 2 ft s3 = x 4 ft

choli [55]

The perimeter of the triangle with those given lengths is $x7-3$

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3 years ago

Question 9 Of 1000 randomly selected cases of lung cancer, 841 resulted in death within 10 years. Construct a 95% two-sided conf

givi [52]

Answer:

0.818335 ≤ p ≤ 0.86366

Step-by-step explanation:

Given that:

Sample size (n) = 1000

Positive lung cancer = 841

n(p) = 841, p(p) = 841/1000 = 0.841

n(1 - p) = 1000 - 841 = 159

1 - p = 0.159

95% confidence interval

For a 95% confidence interval : z = 1.96

P ± z√p(1-p) / n

0.841 ± 1.96 * √0.841(0.159) / 1000

0.841 - (1.96 * 0.0115636) = 0.818335344

0.841 + (1.96 * 0.0115636) = 0.863664656

0.818335 ≤ p ≤ 0.86366

4 0

3 years ago