Answered: Salaries of 33 college graduates who…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Salaries of 33 college graduates who took a statistics course in college have a mean, x, of $65,400. Assuming a standard deviation, σ, of $19,612, construct a 99% confidence interval for estimating the population mean μ.

Salaries of 33 college graduates who took a statistics course in college have a mean, x, of $65,400. Assuming a standard deviation, o, of $19,612,
construct a 99% confidence interval for estimating the population mean μ.
Click here to view a t distribution table.
Click here to view page 1 of the standard normal distribution table.8
Click here to view page 2 of the standard normal distribution table.Ⓡ
<μ<s
(Round to the nearest integer as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1: Introduce the given information

According to the given information,

Sample size, n = 33

Sample mean, $x with bar on top$ = 65400

Population standard deviation, σ = 19612

Confidence level, C = 99% = 0.99

Since, population standard deviation (σ) is known and sample size (n) greater than 30. So we use standard normal distribution.

Using formula,

$C o n f i d e n c e space i n t e r v a l equals x with bar on top plus-or-minus fraction numerator Z subscript c cross times sigma over denominator square root of n end fraction$

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Salaries of 33 college graduates who took a statistics course in college have a​ mean, x​, of $65,400. Assuming a standard​ deviation, σ​, of ​$19,612​, construct a 99​% confidence interval for estimating the population mean μ.

Salaries of 33 college graduates who took a statistics course in college have a mean, x, of $65,400. Assuming a standard deviation, σ, of $19,612, construct a 99% confidence interval for estimating the population mean μ.