Please help me!! Thanks guys!! (-2) the power of -4

1 answer:

7 0

Answer: 1/16

Explanation: turn the Negative 2 into a positive because a (-) base raised to an even power equals (+) to get 2^-4. Afterwards use the formula a^-n=1/a^n to get a^-n= 1/2^4 and 2 to the power of 4 is 16 because 4 times itself is 16 with that it gives you the answer of 1/16. I know this is a bit confusing lol but I hope that helps! Have a good day :))

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In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

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Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

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

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: