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soldier1979 [14.2K]
3 years ago
5

Alpha cube minus beta cube​

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
6 0

Answer:

a³-b³=(a-b)³+3ab(a-b)

          or

(a-b)(a²+b²+ab

Step-by-step explanation:

:/

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A simple random sample (SRS) of 150 is taken from a population with a 0.6 proportion of success. An independent SRS of 250 is ta
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Answer:

SE_{\hat p_1 -\hat p_2}= \sqrt{\frac{0.6(1-0.6)}{150}+\frac{0.3(1-0.3)}{250}}= 0.0494

Step-by-step explanation:

For this case we have the following data:

n_1 =150 represent the random sample 1 selected

\hat p_1 =0.6 represent the proportion of success for the sample 1 selected

n_2 =250 represent the random sample 2 selected

\hat p_2 =0.3 represent the proportion of success for the sample 2 selected

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n_1 p_1  =90 \geq 10, n_1 (1-p_1)=60 \geq 10

n_2 p_2  =75 \geq 10, n_2 (1-p_2)=175 \geq 10

We have the randomization condition and we assume that the two samples are <10% of the entire population size.

So then we can use the following distribution for the proportions:

p \sim N( \hat p, \sqrt{\frac{\hat p (1-\hat p)}{n}})

For this case we want to find the distribution for the difference of these two proportions and we have this:

p_1 -p_2 \sim N (\hat p_1 -\hat p_2 , \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}})

So then the dtandard deviation would be given by:

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