Answered: The data below is a random sample of…

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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The data below is a random sample of students from high school and the number of text messages sent and received over a two-day period. Some information for the data:

sample mean: 43.7333333 sample standard deviation: 38.29857638 and n = 15

0 5 6 6 11 20 28 28 44 73 78 83 90 96 98

a) Check the requirements. Hint: construct a boxplot of the data. Is it appropriate to perform a hypothesis test?

b) If appropriate, perform a hypothesis test to determine whether the mean number of text messages sent is less than 44. (Hint: Complete the "State, Do, and Conclude part). Use the α = 0.05 level.

c) What would it mean to make a Type I error in this situation?

d) What would it mean to make a Type II error?

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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