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ki77a [65]
2 years ago
11

Prove algebraically that n^2-2-(n-2)^2 is always even

Mathematics
2 answers:
Juliette [100K]2 years ago
6 0

Answer:

It is even because it is equal to 2(2n-3) so you can divide it by two and get (2n-3)

Step-by-step explanation:

{n}^{2}  - 2 - ( {n}^{2}  + 4 - 4n) =  \\  {n}^{2}  - 2 - {n}^{2}   - 4  +  4n = \\ 4n - 6 = 2(2n - 3)

tresset_1 [31]2 years ago
3 0

Step-by-step explanation:

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Callaway is thinking about entering the golf ball market. The company will make a profit if its market share is more than 20%. A
Vedmedyk [2.9K]

Answer:

z=\frac{0.224 -0.2}{\sqrt{\frac{0.2(1-0.2)}{624}}}=1.499  

p_v =P(Z>1.499)=0.0669  

If we compare the p value obtained and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly higher than 0.2 or 20%.  

Step-by-step explanation:

How would you make the decision if you were Callaway management? Would you use hypothesis testing?

The best way to test the claim if with a proportion test. The procedure is explained below.

1) Data given and notation

n=624 represent the random sample taken

X=140 represent the golf ball purchasers will buy a Callaway golf ball

\hat p=\frac{140}{624}=0.224 estimated proportion of golf ball purchasers will buy a Callaway golf ball

p_o=0.2 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is more than 0,2 or 20%:  

Null hypothesis:p\leq 0.2  

Alternative hypothesis:p > 0.2  

When we conduct a proportion test we need to use the z statistic, 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.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.224 -0.2}{\sqrt{\frac{0.2(1-0.2)}{624}}}=1.499  

4) 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 significance level is not provided but let's assume \alpha=0.05. 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>1.499)=0.0669  

If we compare the p value obtained and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly higher than 0.2 or 20%.  

8 0
3 years ago
Please answer all 3 for 20 points
zalisa [80]
7
6
1/16
Hope this helps
8 0
2 years ago
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