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Kay [80]
3 years ago
15

Find the distance d(P1, P2) between the points P1 and P2. P1 = (-5,3) P2 = (2,4) d(P1,P2) = (Simplify your answer. Type an exact

answer, using radicals as needed.)
Mathematics
1 answer:
Reptile [31]3 years ago
7 0

Answer:

distance between two points is

5\sqrt{2}

Step-by-step explanation:

the distance d(P1, P2) between the points P1 and P2

Use distance formula

D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

P1 = (-5,3) is (x1,y1)  P2 = (2,4) is (x2,y2)

Plug in the values in the distance formula

D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\D= \sqrt{(2+5)^2+(4-3)^2}\\D= \sqrt{(7)^2+(1)^2}\\\\D= \sqrt{50}\\D=5\sqrt{2}

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Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

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\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

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The degrees of freedom are given by:  

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p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have 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 mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

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