Question

10,000 people were asked about their taste for hot and iced coffee. Of the 10 thousand people, 4 thousand were women, of which 3 thousand like iced coffee, the rest like hot coffee. Of the men, 4 thousand like iced coffee, the rest like hot coffee. Use a 95% confidence level to establish a confidence interval for the proportion of the population of women who like hot coffee.

299

likes
1493 views

Answer to a math question 10,000 people were asked about their taste for hot and iced coffee. Of the 10 thousand people, 4 thousand were women, of which 3 thousand like iced coffee, the rest like hot coffee. Of the men, 4 thousand like iced coffee, the rest like hot coffee. Use a 95% confidence level to establish a confidence interval for the proportion of the population of women who like hot coffee.

Expert avatar
Seamus
4.9
96 Answers
Para establecer un intervalo de confianza para la proporción de mujeres que prefieren café caliente, podemos utilizar la fórmula del intervalo de confianza para una proporción:

\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

Donde:

- \hat{p} es la proporción muestral de mujeres que gustan de café caliente.
- Z es el valor crítico de la distribución normal estándar para el nivel de confianza del 95%, que es aproximadamente 1.96.
- n es el tamaño de la muestra, que en este caso es el total de mujeres encuestadas, es decir, 4000.

Primero, calculemos \hat{p} :
\hat{p} = \frac{\text{número de mujeres que gustan de café caliente}}{\text{total de mujeres encuestadas}} = \frac{1000}{4000} = 0.25

Ahora sustituimos los valores en la fórmula del intervalo de confianza:
\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = 0.25 \pm 1.96 \sqrt{\frac{0.25(0.75)}{4000}}

Calculamos el margen de error:
ME=1.96\sqrt{\frac{0.25(0.75)}{4000}}\approx0.0134

Por lo tanto, el intervalo de confianza del 95% para la proporción de mujeres que gustan de café caliente es:
0.25\pm0.0134

\textbf{Intervalo de Confianza:}(0.237,0.263)

Frequently asked questions (FAQs)
What is the equivalent value, in radians, of an angle that measures 60 degrees?
+
Math question: What is the result of multiplying the vector (2, 3, -4) by the vector (-1, 5, 2)?
+
Math question: What is the integral of e^(2x) from 0 to 1 using the standard formulas of integrals?
+
New questions in Mathematics
Solution to the equation y'' - y' - 6y = 0
Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.
Using the integration by parts method, calculate the integral of [x².ln(1/x)]dx: x 4 /4 x³/6 x 4 /8 x³/3 x 4 /6
The equation of the circle that passes through (5,3) and is tangent to the abscissa axis at x=2 is a.(x-2)^2 (y 3)^2 = 9 b.(x-2)^2 (y-3)^2 = 9 c.(x-2)^2 (y-3)^2 = 4 d.(x-2)^2 (y 1)^2 = 4 e.(x-2)^2 (y-1)^2 = 4
Sean must chose a 6- digit PIN number for his online banking account.Each digit can be chosen from 0 to 9. How many different possible PIN numbers can sean chose.
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
41/39 - 1/38
A warehouse employs 23 workers on first​ shift, 19 workers on second​ shift, and 12 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first ​-shift workers.
28 is 92 percent of what?
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
TEST 123123+1236ttttt
Two minus log 3X equals log (X over 12)
The population of Pittsburgh, Pennsylvania, fell from 520,117 in 1970 to 305,704 in 2010. Write an exponential function P(t) modeling the population t years after 1970. Round the growth factor to the nearest tem thousandth.
Solve equations by equalization method X-8=-2y 2x+y=7
A cell phone company offers two calling plans. Plan A: $20 per month plus 5 cents for each minute, or Plan B: $30 per month plus 3 cents for each minute. [2] Write an equation to describe the monthly cost (a) C (in $) in terms of the time m (in minutes) of phone calls when Plan A is applied.
factor the polynomial completely over the set of complex numbers b(x)=x^4-2x^3-17x^2+4x+30
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
the product of a 2-digit number and a 3-digit number is about 50000, what are these numbers
Determine the general solution of the equation y′+y=e−x .
8(x+4) -4=4x-1