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Nadya [2.5K]
3 years ago
5

What's the distance between (-3,2) and (3,-9)

Mathematics
1 answer:
Triss [41]3 years ago
6 0
17, -3 and 3 are 6apart, -9 and 2 are 11 apart, 6 + 11=17
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In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently
Allushta [10]

Answer:

Null hypothesis:p_{1} - p_{2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)(\frac{1}{800}+\frac{1}{800})}}=-1.182    

p_v =2*P(Z  

Comparing the p value with the significance level given \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 say that we don't have significant difference between the two proportions.  

Step-by-step explanation:

1) Data given and notation  

X_{1}=311 represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

X_{2}=334 represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

n_{1}=800 sample 1

n_{2}=800 sample 2

p_{1}=\frac{311}{800}=0.389 represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

p_{2}=\frac{334}{800}=0.418 represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

\alpha=0.05 significance level given

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions, the system of hypothesis would be:  

Null hypothesis:p_{1} - p_{2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{311+334}{800+800}=0.403  

3) Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)(\frac{1}{800}+\frac{1}{800})}}=-1.182    

4) Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z  

Comparing the p value with the significance level given \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 say that we don't have significant difference between the two proportions.  

6 0
3 years ago
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