Question

In the province of Jaén there are 50 thousand 523 homes, of which 24 thousand 882 are of the urban area. It is desired to know the status of the same, knowing that by studies previous p= 0.60 How many homes should be chosen in each area, using a level 95% confidence level, and a 6% error?

82

likes
410 views

Answer to a math question In the province of Jaén there are 50 thousand 523 homes, of which 24 thousand 882 are of the urban area. It is desired to know the status of the same, knowing that by studies previous p= 0.60 How many homes should be chosen in each area, using a level 95% confidence level, and a 6% error?

Expert avatar
Jon
4.6
97 Answers
To determine the sample size required using the given parameters, we use the formula for a stratified sample:

1. Determine the total number of homes and the number in urban and rural areas:
Total homes: N = 50523
Urban homes: N_1 = 24882
Rural homes: N_2 = 50523 - 24882 = 25641

2. Proportion of the sample from each stratum (urban and rural):
Urban: W_1 = \frac{N_1}{N} = \frac{24882}{50523}
Rural: W_2 = \frac{N_2}{N} = \frac{25641}{50523}

3. Use the formula for the sample size with a given confidence level and margin of error, the formula for sample size n is:
n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right)

where:
- Z is the Z-value for a 95% confidence level (1.96),
- p is the estimated proportion (0.60),
- E is the desired margin of error (0.06).

4. Calculate the sample size:
n = \left( \frac{1.96^2 \cdot 0.60 \cdot (1-0.60)}{0.06^2} \right)
n = \left( \frac{1.96^2 \cdot 0.60 \cdot 0.40}{0.0036} \right)
n \approx 256

5. Allocate the sample size proportionally among strata (rounded to the nearest whole number):
Urban: n_1 = W_1 \cdot n = \frac{24882}{50523} \cdot 256 \approx 126
Rural: n_2 = W_2 \cdot n = \frac{25641}{50523} \cdot 256 \approx 130

Answer: Total sample size is 256 , with 126 homes from the urban area and 130 homes from the rural area.

Frequently asked questions (FAQs)
Math Question: Solve the equation y = 3^x for x, and graph the exponential function.
+
What is the equation of a line with a slope of -2 and a y-intercept of 3?
+
Math question: Find the limit as x approaches infinity of (e^x - x) / (e^x + x).
+
New questions in Mathematics
How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?
I) Find the directional derivative of 𝑓(𝑥, 𝑦) = 𝑥 sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-axis.
By differentiating the function f(x)=(x³−6x)⁷ we will obtain
3x+5y=11 2x-3y=1
A, B, C and D are numbers; If ABCD = 23, What is the result of ABCD BCDA CDAB DABC operation?
7273736363-8
Determine the momentum of a 20 kg body traveling at 20 m/s.
Supposed 60% of the register voters in a country or democrat. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64% round your answer to four decimal places
The expected market return is 13,86% and the risk free rate 1%. What would then be the risk premium on the common stocks of a company which beta is 1,55? (in %, 2 decimal places)
2x2 and how much?
-3(-4x+5)=-6(7x-8)+9-10x
TEST 123123+1236ttttt
Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict. Model the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.
1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?
Salut👋🏻 Appuie sur "Créer une nouvelle tâche" pour envoyer ton problème de mathématiques. Un de nos experts commencera à travailler dessus immédiatement !
Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculation P (B)
t+72/t=-17
f(r) = 1/r+9 find f(x^2) + 1
In an experiment to assess the effect of listening to audiobooks while driving, participants were asked to drive down a straight road in a driving simulator. The accompanying data on time (in milliseconds) to react when a pedestrian walked into the street for 10 drivers listening to an audiobook are consistent with summary statistics and graphs that appeared in the paper "Good Distractions: Testing the Effect of Listening to an Audiobook on Driving Performance in Simple and Complex Road Environments."† (Round your answers to four decimal places.) 1,018 1,007 1,054 988 937 1,030 1,065 1,011 860 1,106 A button hyperlink to the SALT program that reads: Use SALT. Calculate the variance for this data set. 7437.7333 Incorrect: Your answer is incorrect. Calculate the standard deviation for this data set. 86.2022 Incorrect: Your answer is incorrect.
Suppose a car license plate consists of 2 letters and two digits of which the first cannot be zero. How many different plates can be engraved? consider only 26 letters and 10 digits draw an example of this.