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 6 794.6 792.5 794.2 794.4 790.8 793.8 B 800.1 789.8 794.4 793.5 796.0 793.4 (a) Why are these matched-pairs data? A. Two measurements (A and B) are taken on the same round. O B. All the measurements came from rounds fired from the same gun. O C. The measurements (A and B) are taken by the same instrument. O D. The same round was fired in every trial. (b) Is there a difference in the measurement of the muzzle velocity between device A and device B at the a = 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 d, = A, - B,. ldentify the null and alternative hypotheses. Ho: Ha = 0 H: Ha * 0 Determine the test statistic for this hypothesis test. to = -0.83 (Round to two decimal places as needed.) Find the P-value. P-value = (Round three decimal places as needed.) %3D

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter1: Expressions And Functions
Section1.5: Descriptive Modeling And Accuracy
Problem 4CYU
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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           | 794.6| 792.5| 794.2| 794.4| 790.8| 793.8|
| B           | 800.1| 789.8| 794.4| 793.5| 796.0| 793.4|

(a) Why are these matched-pairs data?
- A (correct answer): Two measurements (A and B) are taken on the same round.
- B: All the measurements came from rounds fired from the same gun.
- C: The measurements (A and B) are taken by the same instrument.
- D: The same round was fired in every trial.

(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 = 0
- H₁: μd ≠ 0

Determine the test statistic for this hypothesis test.
- t₀ = -0.83 (Round to two decimal places as needed.)

Find the P-value.
- P-value = 0.443 (Round to three decimal places as needed.)
Transcribed Image Text: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 | 794.6| 792.5| 794.2| 794.4| 790.8| 793.8| | B | 800.1| 789.8| 794.4| 793.5| 796.0| 793.4| (a) Why are these matched-pairs data? - A (correct answer): Two measurements (A and B) are taken on the same round. - B: All the measurements came from rounds fired from the same gun. - C: The measurements (A and B) are taken by the same instrument. - D: The same round was fired in every trial. (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 = 0 - H₁: μd ≠ 0 Determine the test statistic for this hypothesis test. - t₀ = -0.83 (Round to two decimal places as needed.) Find the P-value. - P-value = 0.443 (Round to three decimal places as needed.)
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