To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 41 feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 42 feet. Assume the population standard deviation is 4.4 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). (a) Identify the claim and state Ho and Ha. What is the claim? A.The mean braking distance is different for the two makes of automobiles. This is the correct answer. B.The mean braking distance is the same for the two makes of automobiles. C.The mean braking distance is less for Make A automobiles than Make B automobiles. Your answer is not correct. D.The mean braking distance is greater for Make A automobiles than Make B automobiles. Part 2 What are H0 and Ha? Part 3 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are __ (Round to two decimal places as needed. Use a comma to separate answers as needed.) Part 4 What is/are the rejection region(s)? _ Part 5 (c) Find the standardized test statistic z for μ1−μ2. z=_ (Round to two decimal places as needed.) Part 6 (d) Decide whether to reject or fail to reject the null hypothesis. Part 7 (e) Interpret the decision in the context of the original claim. At the_% significance level, there is (insufficient/ suffcient) evidence to (support/ reject) the claim that the mean braking distance for Make A automobiles is (different from /greater than / less than /equal to) the one for Make B automobiles.

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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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is

41 feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is

42 feet. Assume the population standard deviation is 4.4 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e).

(a) Identify the claim and state Ho and Ha.

What is the claim?

A.The mean braking distance is different for the two makes of automobiles.

This is the correct answer.

B.The mean braking distance is the same for the two makes of automobiles.

C.The mean braking distance is less for Make A automobiles than Make B automobiles.

Your answer is not correct.

D.The mean braking distance is greater for Make A automobiles than Make B automobiles.

Part 2

What are H0 and Ha?

Part 3

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is/are ______

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Part 4

What is/are the rejection region(s)?

_______

Part 5

z=_____

(Round to two decimal places as needed.)

Part 6

(d) Decide whether to reject or fail to reject the null hypothesis.

Part 7

(e) Interpret the decision in the context of the original claim.

At the___% significance level, there is (insufficient/ suffcient) evidence to (support/ reject) the claim that the mean braking distance for Make A automobiles is (different from /greater than / less than /equal to) the one for Make B automobiles.

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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