The following data represent the muzzle velocity (in feet per second) of rounds fired from a 155-mm gun. For each round, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. Complete parts (a) through (d) below. Observation 1 2 3 4 5 6 A 791.7 791.7 794.2 792.1 792.5 792.3 B 800.2 788.4 797.7 791.5 800.4 789.6 1. Why are these matched-pairs data? A.Two measurements (A and B) are taken on the same round. B.The same round was fired in every trial. C. The measurements (A and B) are taken by the same instrument. D. All the measurements came from rounds fired from the same gun. b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let di=Ai−Bi. Identify the null and alternative hypotheses. H0: μd ▼ equals= greater than> not equals≠ less than< enter your response here H1: μd ▼ greater than> less than< not equals≠ equals= enter your response here Determine the test statistic for this hypothesis test. t Subscript 0=enter your response here (Round to two decimal places as needed.) Find the critical value(s) for this hypothesis test. Round to two decimal places as needed.) What is your conclusion regarding H0? ▼ Reject Do not reject H0. There ▼ is is not sufficient evidence at the α=0.01 level of significance to conclude that there is a difference in the measurements of velocity between device A and device B. c) Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. The confidence interval is (__,__) Interpret the confidence interval. A. One can be 99% confident that the mean difference in measurement is 0.01. B. One can be 99% confident that the mean difference in measurement is 0. C. One can be 1% confident that the mean difference in measurement lies in the interval found above. D. One can be 99% confident that the mean difference in measurement lies in the interval found above.

The following data represent the muzzle velocity (in feet per second) of rounds fired from a 155-mm gun. For each round, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. Complete parts (a) through (d) below. Observation 1 2 3 4 5 6 A 791.7 791.7 794.2 792.1 792.5 792.3 B 800.2 788.4 797.7 791.5 800.4 789.6 1. Why are these matched-pairs data? A.Two measurements (A and B) are taken on the same round. B.The same round was fired in every trial. C. The measurements (A and B) are taken by the same instrument. D. All the measurements came from rounds fired from the same gun. b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let di=Ai−Bi. Identify the null and alternative hypotheses. H0: μd ▼ equals= greater than> not equals≠ less than< enter your response here H1: μd ▼ greater than> less than< not equals≠ equals= enter your response here Determine the test statistic for this hypothesis test. t Subscript 0=enter your response here (Round to two decimal places as needed.) Find the critical value(s) for this hypothesis test. Round to two decimal places as needed.) What is your conclusion regarding H0? ▼ Reject Do not reject H0. There ▼ is is not sufficient evidence at the α=0.01 level of significance to conclude that there is a difference in the measurements of velocity between device A and device B. c) Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B. The confidence interval is (,) Interpret the confidence interval. A. One can be 99% confident that the mean difference in measurement is 0.01. B. One can be 99% confident that the mean difference in measurement is 0. C. One can be 1% confident that the mean difference in measurement lies in the interval found above. D. One can be 99% confident that the mean difference in measurement lies in the interval found above.

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

Observation	1	2	3	4	5	6
A	791.7	791.7	794.2	792.1	792.5	792.3
B	800.2	788.4	797.7	791.5	800.4	789.6

1. Why are these matched-pairs data?

A.Two measurements (A and B) are taken on the same round.

B.The same round was fired in every trial.

C. The measurements (A and B) are taken by the same instrument.

D. All the measurements came from rounds fired from the same gun.

b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the

α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

Let

di=Ai−Bi.

Identify the null and alternative hypotheses.

H0:

μd

▼

equals=

greater than>

not equals≠

less than<

enter your response here

H1:

μd

▼

greater than>

less than<

not equals≠

equals=

enter your response here

Determine the test statistic for this hypothesis test.

t Subscript 0=enter your response here

(Round to two decimal places as needed.)

Find the critical value(s) for this hypothesis test.

Round to two decimal places as needed.)

What is your conclusion regarding H0?

▼

Reject

Do not reject H0. There

▼

is not

sufficient evidence at the α=0.01
level of significance to conclude that there is a difference in the measurements of velocity between device A and device B.

c) Construct a 99% confidence interval about the population mean difference. Compute the difference as device A minus device B.

The confidence interval is (__,__)

Interpret the confidence interval.

A. One can be 99% confident that the mean difference in measurement is 0.01.

B. One can be 99% confident that the mean difference in measurement is 0.

C. One can be 1% confident that the mean difference in measurement lies in the interval found above.

D. One can be 99% confident that the mean difference in measurement lies in the interval found above.

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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