Answered: You decide to flip a coin each day to…

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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Question

You decide to flip a coin each day to decide which route to take to school: highway or back roads. In a random sample of 15 days that you take the highway, the mean travel time was 22 minutes with a standard deviation of 4 minutes. In a random sample of 15 days that you take the back roads, the sample mean was 25 minutes with a standard deviation of 2 minutes. Assume that each sample is approximately normally distributed.

a. Perform all 7 steps of hypothesis testing to determine if there is a difference in the mean travel time between
the two routes, at α = 0.05.
b. Find and interpret a 95% confidence interval for the difference in two means. How large might the difference
in means be?

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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