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Description: A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 137 students who averaged 28.8 texts per day. The standard deviation was 17.9 texts. Round answers to

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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A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 137 students who averaged 28.8 texts per day. The standard deviation was 17.9 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a (T/Z) distribution.

b. With 98% confidence the population mean number of texts per day is between__ and__ texts.

c. If many groups of 137 randomly selected members are studied, then a different confidence interval would be produced from each group. About__ percent of these confidence intervals will contain the true population number of texts per day and about ___percent will not contain the true population mean number of texts per day.

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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It is defined as the range which contains the value of true population parameter. The confidence interval is constructed for various population parameters like population mean, population standard deviation and so on.
The confidence interval can be interpreted as : With a stated level of confidence, it can be said that the true population parameter for which confidence interval is constructed lies with the obtained confidence interval.

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