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
97 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)
Find the x-value when the square root function f(x) = √x is equal to 5.
+
Math Question: Solve the cubic equation x^3 + 5x^2 - 2x - 10 = 0. Find all real roots.
+
What is the factored form of x^2 - 9x + 20?
+
New questions in Mathematics
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
a to the power of 2 minus 16 over a plus 4, what is the result?
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
1 + 1
Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;
For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight
The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?
(6.2x10^3)(3x10^-6)
What is the appropriate measurement for the weight of an African elephant?
Primes are numbers divisible only by 1 and themselves; There are infinitely many prime numbers and the first ones are 2, 3, 5, 7, 11, 13, 17, 19, 23, .... Consider a 12-sided die, with the faces numbered from 1 to 12. Out of 4 rolls, the probability that only the first three numbers are primes is:
User Before the election, a poll of 60 voters found the proportion who support the Green candidate to be 25%. Calculate the 90% confidence interval for the population parameter. (Give your answers as a PERCENTAGE rounded to TWO DECIMAL PLACES: exclude any trailing zeros and DO NOT INSERT THE % SIGN) Give the lower limit of the 90% confidence interval Give the upper limit of the 90% confidence interval
With the aim of identifying the presence of the feline leukemia virus (FeLV), blood samples were collected from cats sent to a private veterinary clinic in the city of Belo Horizonte. Among the animals treated, it was possible to observe that age followed a Normal distribution with a mean of 4.44 years and a standard deviation of 1.09 years. Considering this information, determine the value of the third quartile of the ages of the animals treated at this veterinary clinic. ATTENTION: Provide the answer to exactly FOUR decimal places
How much does the average college student spend on food per month? A random sample of 50 college students showed a sample mean $670 with a standard deviation $80. Obtain the 95% confidence interval for the amount college students spend on food per month.
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
We have received our p&l statement back from accounts. The board has asked for an innovation hub. What items should we prioritise reviewing to decide if we can afford an innovation hub?
The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? Produce an algebraic solution. Guess and check is acceptable.
Let I be an interval and let f : I → R be a continuous function such that f(I) ⊂ Q. Show (in symbols) that f is constant.
In a school playground When going out for recess, 80 men and 75 women coexist, the Patio measures 10 meters For 40 meters (what will be the population density in the break
Let f(x)=-1/2x+5 evaluate f(-6)

You might be interested in