Mathematics, 29.05.2020 00:00 catsareokiguess

A certain forum reported that in a survey of 2004 American adults, 23% said they believed in astrology. (a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.)

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The confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology is;

CI = (0.206, 0.254)

We want to find confidence interval at confidence level of 99%. The formula to find confidence level when given proportions like we are given in this question is;

CI = p^ ± (z_α/2)√(p^(1 - p^)/n)

We are given;

p^ = 23% = 0.23

n = 2004

Now,the critical value z_α/2 for confidence level of 99% is gotten from tables to be 2.576.

Thus;

CI = 0.23 ± 2.576√(0.23(1 - 0.23)/2004)

CI = 0.23 ± 0.024

CI = (0.23 - 0.024), (0.23 + 0.024)

CI = (0.206, 0.254)

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Answer from: rhlalbin

The 99% confidence level for the proportion of all adult Americans who believe in astrology is (0.206, 0.254).

Step-by-step explanation:

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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 2004, \pi = 0.23$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so Z = 2.575 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 - 2.575\sqrt{\frac{0.23*0.77}{2004}} = 0.206$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 + 2.575\sqrt{\frac{0.23*0.77}{2004}} = 0.254$

The 99% confidence level for the proportion of all adult Americans who believe in astrology is (0.206, 0.254).

Answer from: Quest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

Answer from: Quest

51-50

step-by-step explanation:

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