In 2011, the number of text messages sent and received by teenage girls (ages 12 – 18) was strongly right skewed. The mean number of messages sent and received each day was 165 with a standard deviation of 45 messages. Suppose we assume teenage boys (ages 12 – 18) send and receive the same number of messages daily. Completely describe the sampling distribution of the sample mean number of text messages sent and received when samples of 296 teenage boys are selected.Using the distribution described in part a, what is the probability of observing a sample mean of 161.082 or less?Classify the probability found in part b using the rule of thumb discussed in class.Based on the probability found, what conclusion can be reached?

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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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In 2011, the number of text messages sent and received by teenage girls (ages 12 – 18) was strongly right skewed. The mean number of messages sent and received each day was 165 with a standard deviation of 45 messages. Suppose we assume teenage boys (ages 12 – 18) send and receive the same number of messages daily.

Completely describe the sampling distribution of the sample mean number of text messages sent and received when samples of 296 teenage boys are selected.
Using the distribution described in part a, what is the probability of observing a sample mean of 161.082 or less?
Classify the probability found in part b using the rule of thumb discussed in class.
Based on the probability found, what conclusion can be reached?

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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