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Mnenie [13.5K]
3 years ago
10

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a populat

ion standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
What is the alternative and null hypotheses?
What is the test statistic?
What is the p-value?
What is your conclusion about the stated hypotheses at a 95% confidence level?
Mathematics
1 answer:
eimsori [14]3 years ago
3 0

Answer:

t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2      

p_v =P(t_{15}>2)=0.0320  

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.  

Step-by-step explanation:

1) Data given and notation      

\bar X=25 represent the sample mean      

s=2 represent the standard deviation for the sample      

n=16 sample size      

\mu_o =24 represent the value that we want to test    

\alpha 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)  

Confidence =0.95 or 95%

\alpha=0.05

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is higher than 24, the system of hypothesis would be:      

Null hypothesis:\mu \leq 24      

Alternative hypothesis:\mu > 24      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2      

Calculate the P-value      

First we need to calculate the degrees of freedom given by:  

df=n-1=16-1=15  

Since is a one-side upper test the p value would be:      

p_v =P(t_{15}>2)=0.0320  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.      

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Ratio Question;
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*Given

Money of Phoebe            - 3 times as much as Andy

Money of Andy                - 2 times as much as Polly

Total money of Phoebe,  - £270

   Andy and Polly

*Solution

Let

B - Phoebe's money

A - Andy's money

L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,

                 B + A + L  = £270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as

 

                 B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                 A = 2L                           (EQUATION 2)

4. This means that Phoebe has ____ as much money as Polly,

                B = 3A

                B = 3 x (2L)

                B = 6L                            (EQUATION 3)

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,

                 6L + 2L + L = £270

                               9L = £270

                                 L = £30

So, Polly has £30.

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.

                 A = 2L                          

                 A = 2(£30)

                 A = £60

Andy has £60

                 B = 6L                        

                 B = 6(£30)

                 B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.

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Firlakuza [10]

Answer:

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Step-by-step explanation:

Let's take two points from given information (2006, 90000) and (2010, 135000).

Now, use slope formula to find slope.

Slope =\frac{y2-y1}{x2-x1}

Use the two points to find average rate of change (slope)

Average rate of change =\frac{135000-90000}{2010-2006}

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Average rate of change = $11250 per year.

6 0
2 years ago
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