A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims "graded150"on the sidewall of the tire. A random sample ofn=19indicates a sample mean tread wear index of148.7and a sample standard deviation of22.3.Complete parts (a) through (c).a.Assuming that the population of tread wear indexes is normally distributed, construct a90%confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name. 139.83139.83≤μ≤157.57157.57(Round to two decimal places as needed.) c.Explain why an observed tread wear index of158for a particular tire is not unusual, even though it is outside the confidence interval developed in (a). A.It is not unusual because it is only0.42standard deviations above the sample mean. B.It is not unusual because it is just outside the confidence interval. C.It is not unusual because it is only0.02standard deviations above the confidence interval. D.It is not unusual because it is actually in the confidence interval.

Confidence interval for population mean is: C.I.=x±tα/2,n-1sn

Answered: A consumer organization wants to…

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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A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims "graded

150"

on the sidewall of the tire. A random sample of

n=19

indicates a sample mean tread wear index of

148.7

and a sample standard deviation of

22.3.

Complete parts (a) through (c).

a.	Assuming that the population of tread wear indexes is normally distributed, construct a 90% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name.

139.83139.83≤μ≤157.57157.57

(Round to two decimal places as needed.)

c.	Explain why an observed tread wear index of 158 for a particular tire is not unusual, even though it is outside the confidence interval developed in (a).

It is not unusual because it is only

0.42

standard deviations above the sample mean.

It is not unusual because it is just outside the confidence interval.

It is not unusual because it is only

0.02

standard deviations above the confidence interval.

It is not unusual because it is actually in the confidence interval.

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