Answered: Constructing a Confidence Interval when…

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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Constructing a Confidence Interval when the Population σσ is Known
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of 3 points. A random sample of 36 scores is taken and gives a sample mean of 68. Find a 95% confidence interval estimate for the population mean exam score by providing the following information.

Constructing a Confidence Interval when the Population o is Known
Suppose scores on exams in statistics are normally distributed with an unknown population mean and a
population standard deviation of 3 points. A random sample of 36 scores is taken and gives a sample mean
of 68. Find a 95% confidence interval estimate for the population mean exam score by providing the
following information.
Confidence Level
Area in One Tail
Z-Score
50%
0.25
0.674
80%
0.1
1.282
90%
0.05
1.645
95%
0.025
1.96
98%
0.1
2.326
99%
0.005
2.576
(Include two decimal places below)
a. a =
b. 20.025
с. ЕВМ
d. The lower bound of the Confidence Interval is
e. The upper bound of the Confidence Interval is

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 + ...

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