Answered: % confidence interval for the mean…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 112 students who averaged 26.7 texts per day. The standard deviation was 24.5 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ____ distribution.

b. With 95% confidence the population mean number of texts per day is between and ___ texts ____.

c. If many groups of 112 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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