1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
What is 3/4*16/21<br> Simplify fractors
nikklg [1K]

\bf \cfrac{3}{4}\cdot \cfrac{16}{21}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 4}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 7}\implies \cfrac{4}{7}

4 0
3 years ago
The area of a rectangular field is 5695 m².
denpristay [2]

Answer:

85 m

Step-by-step explanation:

5696/67=85

3 0
3 years ago
The lengths of a certain species of fish are approximately normally distributed with a given mean (look at the picture) and stan
tatyana61 [14]
The empirical rule states that approximately 68/95/99.7% of a normal distribution lies within 1/2/3 standard deviations. So the answer is 68%.
6 0
3 years ago
Read 2 more answers
What is the measure of ZA?
ehidna [41]
B. 60°
This is an equilateral triangle, so all angles should be equal. 180/3=60, so you’re answer is 60.
8 0
3 years ago
Table, proportional or non-proportional?
Alexandra [31]
B) is the answer hope this helps
6 0
3 years ago
Other questions:
  • Please help:
    8·1 answer
  • PLEASE HELP GEOMETRY QUESTION!!
    15·1 answer
  • the princaipal at oak school ordered 25 pizzas for the fourth grade claasses share he will deliver an equal number of pizzas to
    10·1 answer
  • A triangle has sides measuring 5 inches and 8 inches. If x represents the length in inches of the third side, which inequality g
    14·2 answers
  • A diameter of a circle has endpoints P(-10,-2) and Q(4,6).
    8·1 answer
  • If you were to describe a reflection of triangle ABC, what information would you need to include in your description?
    8·1 answer
  • How to solve this one​
    14·2 answers
  • Write the standard equation of a circle with center (-1, 4) and radius 5
    15·1 answer
  • The perimeter of a Balcony is 26 ft it is 4 ft wide how long is it?
    14·1 answer
  • Is -13/3 rational or irrational
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!