In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Sample size needed

At least n, in which n is found when $M = 0.09$

We don't know the proportion, so we use $\pi = 0.5$ , which is when we would need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.09\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.09})^{2}$

$n = 118.6$

Rounding up

We need a sample size of least 119

6 0

3 years ago

The Math 123 book includes about 230 pages (not including the back parts of the book). If you aim to complete 65% of all the pag

alina1380 [7]

Answer: 150 pages

Step-by-step explanation:

I usually just multiply the number by the percentage and it works out just fine :)

8 0

3 years ago

A pediatrician wants to conduct a survey to determine if the number of children per family is statistically the same in the Unit

kari74 [83]

Answer:

There is not enough information to know if there is a statistically significant difference in the number of children per family between the three countries.

Step-by-step explanation:

There are other important information that are necessary in order to reach a decisive conclusion. This includes not just the f value only, but the alpha value, f critical value and the p-value after conducting the one way ANOVA.

Since we do not have information about the p value, as well as the alpha value there is no way to compare the effects of all the variables.

Therefore, no decision can be made by the Pediatrician without knowing what the p value is and the apha value is.

8 0

3 years ago