What is the exponential regression equation that fits these data x=-4 y=0.25

Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

7 0

3 years ago

How to find the repeating decimal of 29/13

8_murik_8 [283]

Divide 13 into 29:
2.230769230769....

13 ) 29.0000000
26
—-
3 0 this remainder repeats 6 steps further down
2 6
——
40
39
——
100
91
——
90
78
—
120
11 7
—-
30 which will lead to a recurring decimal because we had remainder 3 at the beginning

6 0

3 years ago

The purpose of this lesson is to learn new math concepts. True False

Fed [463]

True
HOPE THIS HELPS!

4 0

3 years ago

Read 2 more answers

A survey of 347 high school students asked students to describe their

vampirchik [111]

Answer:

Step-by-step explanation:

Conditional relative frequency is a frequency that is obtained in fraction that tells you what particular group has a particular feature.

In the questions above

Total number of high school students = 347

We have 3 groups based on their political tendencies

Liberal

Total number of Liberal students: 95

Total number of male Liberal Students = 27

Total number of female Liberal student = 95 - 27 = 68

Moderate

Total number of moderate students: 128

Total number of female moderate Students = 91

Total number of male moderate students is calculated as = 128 - 91

= 37

Conservative

Total number of conservative students: is not given in the question.

This is calculated as Total number of High school student - ( Total number of Liberal students + Total number of Moderate students)

347- (95+128) = 347- 223

= 124

Total number of female conservative Students= 93

Total number of male conservative students was not given in the question. Therefore it is calculated as = 124 -93 = 31

To determine the conditional relative frequency of males = Total number of high school male students in the school ÷ Total number of high school students in the school

Total number of male high school students is calculated as = Number of male Liberal students + Number of male Moderate students + Number of male Conservative students.

= 27 + 37 + 31

= 95 male high school students.

Hence the Conditional relative frequency of males = 95/347

3 0

3 years ago

Which of the following can help humans conserve mineral resources?

yarga [219]

Answer: by utilizing renewable resources.

Step-by-step explanation:

Example : using hydroelectricity and solar power as sources of energy may conserve mineral resources such as coal.

5 0

3 years ago