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Georgia [21]
3 years ago
7

A new radar device is being considered for a certain missile defense system. The system is checked by experimenting with aircraf

t in which a kill or a no kill is simulated. Two research group A and B participated the simulation, and it was found that 63 kills occur out of 100 trials by group A, and 59 kills occur out of 125 trials by group B. Is there a significant difference between the proportions of group A and B's simulation? Use P-value with significance level of 0.05 to draw a conclusion.
Mathematics
1 answer:
adell [148]3 years ago
6 0

Answer:

There is significant difference between the proportions of group A and group B.

Step-by-step explanation:

In this question we need to perform an hypothesis test on the difference of proportions (Δπ) and determine if there is any significant difference between the two proportions.

The null and alternative hypothesis are:

H_0: \Delta \pi=0\\\\H_1: \Delta \pi\neq0

The proportion of group A is p_1=63/100=0.630.

The proportion of group B is p_2=59/125=0.472.

The weighted average of p (to calculate s) is:

p=\frac{n_1*p_1+n_2*p_2}{n_1+n_2}=\frac{100*0.630+125*0.472}{100+125}=\frac{63+59}{100+125}=\frac{122}{225}=0.542

The estimated standard deviation is:

s=\sqrt{\frac{p(1-p)}{n_1}+\frac{p(1-p)}{n_2} } =\sqrt{\frac{0.542(1-0.542)}{100}+\frac{0.542(1-0.542)}{125}} =\sqrt{\frac{0.248}{100} +\frac{0.248}{125} } \\\\s=\sqrt{0.00447} =0.067

Then we can calculate z as

z=\frac{p_1-p_2}{s}=\frac{0.630-0.472}{0.067}=\frac{0.158}{0.067}=2.36

The P-value for z=2.36 is 0.009, which is less that the significance level of 0.05. The effect is significant and the null hypothesis is rejected.

There is significant difference between the proportions of group A and group B.

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The length of segment HJ if H lies at (-1,7) and J lies at (8,-5)​
sukhopar [10]

Answer:

<h3>HJ = 15</h3>

Step-by-step explanation:

To get the length of segment HJ if H lies at (-1,7) and J lies at (8,-5)​, we will use the formula for calculating the distance between two points as shown;

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Answer:

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Step-by-step explanation:

<u><em>Given:</em></u>

<em>Clara is stacking cups; she put 45 plastic cups in the first stack, 38 plastic cups in the second stack, 31 plastic cups in the third stack, and 24 plastic cups in the fourth stack. </em>

<u><em>To Find:</em></u>

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<em>Let's make a table:</em>

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<em>[1 stack]  45 </em>

<em>[2 stack] 38</em>

<em>[3 stack] 31</em>

<em>[4 stack] 24</em>

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<em>[1 stack]  45 ⇒ 7</em>

<em>[2 stack] 38 ⇒ 7 </em>

<em>[3 stack] 31 ⇒ 7 </em>

<em>[4 stack] 24 ⇒ 7 </em>

<em>Hence, each stack is going down by 7.</em>

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<u><em>Kavinsky</em></u>

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