For the following, use a normal distributionor a t-distribution to construct a 95% confidence interval for the populationmean. Justify your decision. If neither distribution can be used, explain why. Ifconvenient, use technology to construct the confidence interval. 25. Sports Cars: Miles per Gallon You take a random survey of 25 sportscars and record the miles per gallon for each. The data are listed below.Assume the miles per gallon are normally distributed.15 27 24 24 20 2124 14 2125 2113 21 25 22 21 25 2422 24 24 22 21 24 2426. ACT Scores In a recent year, the standard deviation of ACT scores forall students was 4.8. The ACT scores for 20 randomly selected studentsare listed below. Assume the test scores are normally distributed. (Source:ACT, Inc.)26 22 23 12 19 25 23 21 25 1017 26 23 24 20 14 21 23 20 2227. Hospital Waiting Times In a random sample of 19 patients at a hospital'sminor emergency department, the mean waiting time (in minutes) beforeseeing a medical professional was 23 minutes and the standard deviation was11 minutes. Assume the waiting times are not normally distributed.

Answered: 25. Sports Cars: Miles per Gallon You…

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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Question

For the following, use a normal distribution or a t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. If convenient, use technology to construct the confidence interval.

25. Sports Cars: Miles per Gallon You take a random survey of 25 sports
cars and record the miles per gallon for each. The data are listed below.
Assume the miles per gallon are normally distributed.
15 27 24 24 20 21
24 14 21
25 21
13 21 25 22 21 25 24
22 24 24 22 21 24 24
26. ACT Scores In a recent year, the standard deviation of ACT scores for
all students was 4.8. The ACT scores for 20 randomly selected students
are listed below. Assume the test scores are normally distributed. (Source:
ACT, Inc.)
26 22 23 12 19 25 23 21 25 10
17 26 23 24 20 14 21 23 20 22
27. Hospital Waiting Times In a random sample of 19 patients at a hospital's
minor emergency department, the mean waiting time (in minutes) before
seeing a medical professional was 23 minutes and the standard deviation was
11 minutes. Assume the waiting times are not normally distributed.

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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