Answered: a socialogist expects the life…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

a socialogist expects the life expenancy of people in africa is different than the life expantancy of people in asia. the data shown in the table below. determine the 95% confidence interval for the difference in the population mean

africa	asia
mean₁= 63.3 yr	mean₂= 65.2
STD₁= 9.1 yr	STD₂= 7.3 yr
n₁=120	n₂= 150

calculate the critical value. use σ=0.05

A) -11.4 < μ₁ - μ₂ < -7.6 B)-12.2< μ₁ - μ₂ < -6.9 C). -13.5< μ₁ - μ₂ < -6.3

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

Step-by-step procedure to obtain the value of using STATKEY:

Choose Normal under Theoretical Distributions.
In Normal Distribution, click Edit Parameters.
Enter mean as 0 and standard deviation as 1 and click Ok.
Click Two-Tail.
Click OK.

Output obtained using the MINITAB software is given below:

Normal Distribution
Reset Plot
Left Tail
Two-TailRight Tail
0.40
0.35
0.30
0.25
0.20
0.025
0.950
0.025
0.15
0.10
0.05
0.00
4.0
1.0
-3.0
1.0
0.0
1.0
3.0
4.0
-1.960
1.960

Step 2

From the output, the value of is 1.96 for 95% confidence.

The 95% confidence interval is obtained as follows:

Sample statistic
ME = (x-
+
п,
п,
(9.1) (7.3)
2
=(63.3-65.2) 1.96f-
120
150
=-1.9+ 2.004
=(-3.904,0.104)

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