Answered: Education influences attitude and…

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

Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 34 U.S. cities. The sample mean for these cities showed that x1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n2 = 30 U.S. cities. The sample mean for these cities showed that x2 = 18.4% of the young adults had attended college. From previous studies, it is known that ?1 = 7.2% and ?2 = 5.6%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use ? = 0.05.

a) What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to two decimal places.)

b) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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

For age 65 and older :

Sample Mean 1 $(\bar X_1)$ =	$15.2$
Population Standard Deviation 1 $(\sigma_1)$ =	$7.2$

For young adults :

Sample Mean 2 $(\bar X_2)$ =	$18.4$
Population Standard Deviation 2 $(\sigma_2)$ =	$5.6$

Null and Alternative Hypotheses :

$\begin{array}{ccl} H_{0} : μ_{1} & \geq & μ_{2} \\ H_{a} : μ_{1} & < & μ_{2} (p o p u l a t i o n m e a n p e r c e n t a g e o f y o u n g a d u l t s w h o a t t e n d e d c o l l e g e i s h i g h e r) \end{array}$