MathMaster logo

MathMaster

  1. Home
  2. general
  3. 1 the following is a simple random sample taken from a population of employees in a company the information that was asked
Question

1. The following is a simple random sample taken from a population of employees in a company. The information that was asked of each person was the monthly salary they had last year measured in dollars. 1200 4500 1340 3100 2500 5100 2100 1300 2300 4100 3200 1200 5200 3500 2600 (a) Determine the sample average wage and the sample standard deviation of the wages of the employees. (b) Determine the standard error of the mean assuming the population is infinite. Find the 95% confidence interval for the average salary of employees. (c) Assuming that the company has a total of 50 employees. How should I change the interval reliable for the average salary of employees? (d) Recalculate the standard error of the mean with correction for finite population. Find the 95% confidence interval for the average employee salary.

264

likes
1321 views

Answer to a math question 1. The following is a simple random sample taken from a population of employees in a company. The information that was asked of each person was the monthly salary they had last year measured in dollars. 1200 4500 1340 3100 2500 5100 2100 1300 2300 4100 3200 1200 5200 3500 2600 (a) Determine the sample average wage and the sample standard deviation of the wages of the employees. (b) Determine the standard error of the mean assuming the population is infinite. Find the 95% confidence interval for the average salary of employees. (c) Assuming that the company has a total of 50 employees. How should I change the interval reliable for the average salary of employees? (d) Recalculate the standard error of the mean with correction for finite population. Find the 95% confidence interval for the average employee salary.

Expert avatar
Tiffany
4.5
103 Answers
(a)
\bar{X} = \frac{\sum X_i}{n} = \frac{44000}{15} = 2933.33 \, \text{dólares}
s = \sqrt{\frac{\sum (X_i - \bar{X})^2}{n-1}} = \sqrt{\frac{25100000}{14}} = 1341.94 \, \text{dólares}

(b)
E_m = \frac{s}{\sqrt{n}} = \frac{1341.94}{\sqrt{15}} = 346.53 \, \text{dólares}
\text{IC}_{95\%} = \bar{X} \pm Z \frac{s}{\sqrt{n}} = 2933.33 \pm 1.96 \cdot 346.53
\text{IC}_{95\%} = (2254.14, 3612.52) \, \text{dólares}

(c)
Dado que la población es finita (50 empleados), el intervalo de confianza debería ser más pequeño debido al factor de corrección de población finita.

(d)
E = \frac{s}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}} = \frac{1341.94}{\sqrt{15}} \sqrt{\frac{50-15}{50-1}} = 316.25 \, \text{dólares}
\text{IC}_{95\%} = \bar{X} \pm Z \cdot E = 2933.33 \pm 1.96 \cdot 316.25
\text{IC}_{95\%} = (2304.21, 3562.46) \, \text{dólares}

Frequently asked questions (FAQs)
Question: What is the volume of a right circular cylinder with a radius of 4 units and height of 6 units?
+
Math Question: Convert 6,450,000,000 to scientific notation.
+
What is the range of the square root function: f(x) = √x, where x ranges from 0 to 100?
+
New questions in Mathematics
A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:40 a.m. Round your answer to four decimal places, if necessary.
Solution to the equation y'' - y' - 6y = 0
A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?
two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?
what is 3% of 105?
The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?
To make brine, José buys 1 kg of salt and pays 12 pesos. If he buys 4 kg, they charge him 48 pesos, but for 100 pesos they sell him 9 kg. What is the constant of proportionality?
Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.
In a laboratory test, it was found that a certain culture of bacteria develops in a favorable environment, doubling its population every 2 hours. The test started with a population of 100 bacteria. After six hours, it is estimated that the number of bacteria will be:
X~N(2.6,1.44). find the P(X<3.1)
The grading on a $159,775 house comes to $3974.75. What percent of the total cost is this? (Express your answer to the nearest hundredth percent.)
Find the equation of a straight line that has slope 3 and passes through the point of (1, 7) . Write the equation of the line in general forms
A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be Normally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and Standard deviation is measured in millimeters. What is the probability that an arbitrary route has a thickness less than 4.00 mm?
To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³
8/9 divided by 10/6
Solve for z: 2z-6=10z+2
4m - 3t + 7 = 16
Marc, Jean and Michelle have traveled a lot. Marc drove twice as much as Jean, but it was Michelle who drove the most with 100km more than Marc. They respected their objective of not exceeding 1350km of distance. How far did John drive?
Sally’s sales for last Sunday were $1,278. That was an increase of 6.5% over her sales for the previous Saturday. What were her sales for the previous Saturday?
A triangle is cut by a line s parallel to the base in such a way that it divides the side of the triangle into parts in the ratio of 2 : 3. Find the other side of the triangle if it is known that the line s divides it into parts whose length is 5 cm.

You might be interested in