Answered: 1.a) If the true textbook cost is $524, what is the z-score and corresponding probability that you’d get a sample with a mean like the one we observed in Sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

The Office of Financial Aid has historical data that indicates the standard deviation of textbook costs is steady from semester to semester at $287. Please use the info provided to answer the 3 subquestions:

1.a) If the true textbook cost is $524, what is the z-score and corresponding probability that you’d get a sample with a mean like the one we observed in Sample A or less? Provide an interpretation for your z-score.

1.b) Using this probability, does the reported value of $524 seem reasonable?

1.c) Should the administrators adjust the value? Justify your recommendation using the statistical support provided

The Office of Financial Aid at the University of Michigan currently quotes the cost of textbooks
for undergraduate students per semester to be
if their estimate is accurate or if this figure needs to be updated before the start of the next
Administrators are interested in verifying
school year. They know that in order to obtain a more realistic estimate they need to rely on
student data, so they have turned to various organizations on campus for help.

Standard
Organization
Mean
Sample Size
Deviation
Sample A
$346
$39
25
Sample B
$286
$47
200
Stats 250
gathered data on the
cost of textbooks for
$129.8
$109.5312
1494
all students currently
lenrolled in the course

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

Since, the question is not properly specified and does not provide a lot of information, the work is done on the basis of intuition, depending upon the information provided.

We see that, true text book cost is $524.

Statistics homework question answer, step 1, image 1

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