Answered: Use a 0.05 level of significance and…

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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A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.

Student	Math	Writing
1	540	474
2	432	380
3	528	463
4	574	612
5	448	420
6	502	526
7	480	424
8	499	459
9	610	615
10	572	541
11	390	329
12	593	613

(a)

Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)

Formulate the hypotheses.

1. H₀: μ_d > 0

H_a: μ_d ≤ 0

2. H₀: μ_d ≤ 0

H_a: μ_d = 0

3. H₀: μ_d ≠ 0

H_a: μ_d = 0

4. H₀: μ_d = 0

H_a: μ_d ≠ 0

5. H₀: μ_d ≤ 0

H_a: μ_d > 0

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

1.Do not reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.

2. Reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.

3. Reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.

4. Do not reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.

(b)

What is the point estimate of the difference between the mean scores for the two tests? (Use math score − writing score.)

What are the estimates of the population mean scores for the two tests?

Math ( )

Writing ( )

Which test reports the higher mean score?

The math test reports a (higher or lower) mean score than the writing test.

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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