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erastova [34]
2 years ago
14

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

hysical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
5 0

Using the z-distribution and the formula for the margin of error, it is found that:

a) A sample size of 54 is needed.

b) A sample size of 752 is needed.

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

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

In which z is the z-score that has a p-value of \frac{1+\alpha}{2}.

The margin of error is of:

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

90% confidence level, hence\alpha = 0.9, z is the value of Z that has a p-value of \frac{1+0.9}{2} = 0.95, so z = 1.645.

Item a:

The estimate is \pi = 0.213 - 0.195 = 0.018.

The sample size is <u>n for which M = 0.03</u>, hence:

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

0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}

\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2

n = 53.1

Rounding up, a sample size of 54 is needed.

Item b:

No prior estimate, hence \pi = 0.05

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

0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}

0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}

\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2

n = 751.7

Rounding up, a sample of 752 should be taken.

A similar problem is given at brainly.com/question/25694087

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Answer:

9.4339 units

Step-by-step explanation:

Here we are given with two coordinates and asked to determine the distance between them.

Here we are going to use the distance formula, which is given as under

D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Where

(x_1,y_1) = (-4,5)

(x_2,y_2) = (4,0)

Replacing these values in the distance formula

D =\sqrt{(-4-4))^2+(5-0)^2}

D =\sqrt{(-8)^2+(5)^2}

D =\sqrt{64+25}

D =\sqrt{89}

D= 9.4339

Hence the distance is 9.4339 units

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3 years ago
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If the legs of an isosceles right triangle have a length of ft, the hypotenuse will have a length of?
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Heart failure is due to either natural occurrences (89%) or outside factors (11%). Outside factors are related to induced substa
Firdavs [7]

Answer:

a) 11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.

b) 0.0871 = 8.71% probability that third patient with heart failure that enters the emergency room is the first one due to outside factors.

c) The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.

Step-by-step explanation:

We have these following probabilities:

89% probability that a patient has heart failure due to natural occurrences.

11% probability that a patient has heart failure due to outside factors.

A) What is the probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors?

We assume that causes of heart failure between individuals are independent, which means that the probabilities are the same for each patient. So:

11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.

B) What is the probability that third patient with heart failure that enters the emergency room is the first one due to outside factors?

First two due to natural occurrences, each with 89% = 0.89 probability.

Third due to outside factors, with 11% = 0.11 probability. So

0.89*0.89*0.11 = 0.0871

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C) What is the mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors?

11% with outside factors, so the mean number of patients before the first with outside factors is given by

m = 1/0.11 = 9.09

The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.

4 0
3 years ago
4/5 of a number is more than 3/4 of the number by 5.find the numbers
Nastasia [14]
4/5 of x -3/4 of x =5
solution by LCM

16x-15x/20 =5
x/20 =5
x=100
<span>answer 100</span>
8 0
3 years ago
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