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 of the interval 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 $Z = 1.96$ .

Estimate the sample size needed if no estimate of p is available so that the confidence interval will have a margin of error of 0.02.

We have to find n, for which M = 0.02.

There is no estimate of p available, so we use $\pi = 0.5$

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}$

$n = 2401$

The sample size needed is 2401.

7 0

3 years ago

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Matthew practiced playing the guitar for 2/3 hours. Natalie practiced playing the guitar 1 3/4 times as long as

belka [17]

Answer:

2/3*(7/4)=7/6 hours

Step-by-step explanation:

7 0

2 years ago

If a cross-country runner runs a 55 kilometer (km) race, how many miles is that? Round your answer to one decimal place.

prohojiy [21]

Answer: 34.2

For everyone 1 kilometer=.621371 so if you times that by 55 you get 34.1754 which rounds to 34.2

5 0

3 years ago

Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] T

Dahasolnce [82]

Answer:

(a) [8, 14]

(b) $8 \leq x \leq 14$

(c)See attachment

Step-by-step explanation:

We want to choose a value of x within 3 units of 11.

(a)Now, 11-3=8 and 11+3=14

The possible values of x ranges is in the closed interval [8,14]

(b) Since x is within 3 units of 11., we have:

$|11-x|\leq3$

Solving the absolute inequality

$-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14$

(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.

5 0

3 years ago

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