What is the P Value Reject H0?Construct a 99% confidence interval about the population mean differenceDraw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)? 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 ≠ 0Determine 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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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter1: Expressions And Functions

Section1.5: Descriptive Modeling And Accuracy

Problem 4CYU

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What is the P Value
Reject H0?
Construct a 99% confidence interval about the population mean difference
Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)?

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.)

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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