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 cube with side length ‘s’ and an edge length of (2s - 3) cm?

Question: What is the equation of the line passing through points (2,5) and (4,11)? (

Math question: What is the smallest positive integer solution to the equation x^n + y^n = z^n for n>2, as stated in Fermat's Last Theorem?

New questions in Mathematics

Find 2 numbers that the sum of 1/3 of the first plus 1/5 of the second will be equal to 13 and that if you multiply the first by 5 and the second by 7 you get 247 as the sum of the two products with replacement solution

the value of sin 178°58'

A drawer contains three pairs of white socks, five pairs of black socks and two pairs of red socks. Caden randomly selects two pairs of socks on his way to the gym. What is the probability that both pairs of socks are black?

58+861-87

Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number

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

What’s 20% of 125?

All the liquid contained in a barrel is distributed into 96 equal glasses up to its maximum capacity. We want to pour the same amount of liquid from another barrel identical to the previous one into glasses identical to those used, but only up to 3/4 of its capacity. How many more glasses will be needed for this?

The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =

calculate the normal vector of line y = -0.75x + 3

I need to know what 20% or £3292.75

The price per night of a suite at the Baglioni Hotel in Venice is 1896 euros, VAT included. The VAT in Italy is 25%. The hotel gets a return of 10% out of the price VAT included. a) What is the amount of VAT paid by the hotel for one

A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall

Solve equations by equalization method X-8=-2y 2x+y=7

Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.

Given the word WEIRD, determine a four-letter offspring that can be formed with the letters of the word written above

Read the “Local Communities as Stakeholders: Does Amazon Really Need Tax Breaks?” example on p. 83 in Ch. 3 of Management: A Practical Introduction. In your response, discuss whether you feel that tax breaks for big companies benefit local communities. Describe ways to attract business to a region without having a negative impact on the larger community.

Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X

Find the orthogonal projection of a point A = (1, 2, -1) onto a line passing through the points Pi = (0, 1, 1) and P2 = (1, 2, 3).

97,210 ➗ 82 division

You might be interested in