When variables are being raised to a power what operation is performed with the exponents?

1 answer:

4 0

First you raise the expressions in the parentheses to their powers. Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).

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There were 324 adults surveyed. Among the participants, the mean number of hours of sleep each night was 7. 5 and the standard d

NeTakaya

The margin of error for 324 adults surveyed with 1.6 standard deviations is 0.1742.

<h3>What is the margin of error?</h3>

The margin of error can be defined as the amount of random sampling error in the results of a survey. It is given by the formula,

$\text{MOE}_{\gamma}=z_{\gamma} \times \sqrt{\frac{\sigma^{2}}{n}}$

$\text{MOE}$ = margin of error

$\gamma$ = confidence level

$z_{\gamma}$ = quantile

σ = standard deviation

n = sample size

As it is given that the sample size of the survey is 324, while the standard deviation of the survey is 1.6.

We know that the value of the z for 95% confidence interval is 1.96. Therefore, using the formula of the standard of error we can write it as,

$\text{MOE}_{\gamma}=z_{\gamma} \times \sqrt{\dfrac{\sigma^{2}}{n}}\\\\\text{MOE}_{\gamma}=1.96 \times \sqrt{\dfrac{1.6^{2}}{324}}\\\\\text{MOE}_{\gamma}=0.1742$