How does the product of powers law apply to finding the power of a power?

1 answer:

7 0

The product of powers tells us about that multiplying the powers with the same number you have simply have to add the exponents,

for example;

=6^3 * 6^3

=6^3 *6^3 (^3+^3) we are just adding the exponents even thou the operation is multiplication.

= 36^6

The power of power tells us about multiplying both the expression including the exponents. Power rule tells us that a power to a power, just multiply the exponents.

for example;

=6^3 * 6^3

=6^3 * 6^3 (^3*^3) we are multiplying both of the expression

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Explain how to perform a two-sample z-test for the difference between two population proportions.

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Point estimate for the difference between two population proportions is the difference between the two sample proportions, written as:

$\hat{p}_1-\hat{p}_2$

and the standard deviation is given by

$\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$

When np and n(1-p) is greater than 5, then the sampling distribution is approximately normal and we can use standard normal methods.

Thus, the propability of a test <span>for the difference between two population proportions is given by

$P(X\ \textless \ x)=P\left(z\ \textless \ \frac{\hat{p}_1-\hat{p}_2}{\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}} \right)$ </span>