Calculate the lower confidence limit (LCL) and upper confidence limit (UCL) of the mean for each of the following.a. x =265,
n=459, σ=50, and α=0.01b. x=180, n=308, σ2equals=100, and α=0.05LCLequals=(Round to two decimal places as needed.)UCLequals=(Round to two decimal places as needed.)b.LCLequals=(Round to two decimal places as needed.)UCLequals=(Round to two decimal places as needed.)
1 answer:
Answer:
a: 258.09
b: 178.88
Step-by-step explanation:
For a: Since n > 30, we use a z-value that corresponds to 0.01, or 99% confidence. This z-value is: 2.575
We have:
x = 265, n = 459, σ = 50. See the calculation for the error and the construction of the confidence interval on the first attached photo
For b: Since n > 30, we use a z-value that corresponds to 0.05, or 95% confidence. This z-value is: 1.96
x = 180, n = 308, σ = 10 (it gives σ² = 100. so σ = 10). See the calculation for the error and the construction of the confidence interval on the second attached photo
You might be interested in
Solution for
It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!
Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.
<u>First way</u>
Let us add to both sides
On the right side for the addition operation, we equate the common denominator by multiplying
Then we combine terms to get
Divide by the coefficient of m, or in other words, multiply both sides by
Finally, the solution is obtained as follows
Simplify fractions, both the numerator and denominator are divided equally by 7.
Convert into mixed fractions, we get:
In decimal form, we get
<u>Second way (a quick way)</u>
Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)
We use the distributive property of multiplication on the left side
or it can also directly lead to
Add 2 to both sides, we get
Divide by the coefficient of m, or in other words, both sides are divided by 4
Or,
Or,
Wanna check the solution into the equation?
Both sides show the same value, so the solution is correct.
Note:
Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:
- adding,
- subtracting,
- multiplying, and/or
- dividing both sides of the equation with the same number.
In the form of fractions, the steps that must be considered are
- equate the denominator,
- simplify fractions, and
- for the final answer, convert fractions to mixed fractions or decimal forms
All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.
<h3>Learn more</h3>- A word problem that forms a single variable linear equation brainly.com/question/1566971
- Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
- Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876
Grade : Middle School
Subject : Mathematics
Chapter : Linear Equation in One Variable
Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal
