tudy was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with a mean of $9171 and a standard deviation of $5539 . Construct a 99% confidence interval for the mean of all such costs. a. Find the critical value: t Subscript alpha divided by 2 Baseline equals nothing (use 3 decimal places) b. State the sample size: n = nothing (give a whole number) c. Calculate the margin of error: E = nothing (round off to a whole number) d. Give the confidence interval: nothing less than mu less thannothing (round off to whole numbers) e. An opponent of seat belt laws believes that seat belts actually cause more harm than good and claims that the mean hospital costs for accident victims who wore seat belts is more than $15,000. Does this data support his claim? Why or why not? A. No, the upper confidence interval limit is less than $15,000 B. Yes, the lower confidence interval limit is greater than $15,000 C. No, the sample mean is about $15,000 D. Yes, the upper confidence interval limit is less than $15,000 f. If we were not told that the distribution appears to be bell-shaped, would we be able to calculate the margin of error using the same formula?

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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tudy was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with a mean of

$9171

and a standard deviation of

$5539

Construct a 99% confidence interval for the mean of all such costs.

a. Find the critical value:

t Subscript alpha divided by 2 Baseline equals

nothing

(use 3 decimal places)

b. State the sample size: n =

nothing

(give a whole number)

c. Calculate the margin of error: E =

nothing

(round off to a whole number)

d. Give the confidence interval:

nothing

less than mu less thannothing

(round off to whole numbers)

e. An opponent of seat belt laws believes that seat belts actually cause more harm than good and claims that the mean hospital costs for accident victims who wore seat belts is more than $15,000. Does this data support his claim? Why or why not?

No, the upper confidence interval limit is less than $15,000

Yes, the lower confidence interval limit is greater than $15,000

No, the sample mean is about $15,000

Yes, the upper confidence interval limit is less than $15,000

f. If we were not told that the distribution appears to be bell-shaped, would we be able to calculate the margin of error using the same formula?

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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