Plagiarism is a growing concern among college and university faculty members, and many universities are now using software tools to detect student work that is not original.An Australian university introduced the use of plagiarism detection software in a number of courses. Researchers surveyed 171 students enrolled in those courses.† In the survey, 58 of the 171 students indicated that they believed that the use of plagiarism-detection software unfairly targeted students.Assuming it is reasonable to regard the sample as representative of students at this university, does the sample provide convincing evidence that more than one-third of the students at the university believe that the use of plagiarism-detection software unfairly targets students?Withp = proportion of all students at the university who believe that the use of plagiarism-detection software unfairly targets studentsthe relevant hypotheses areH0: p = 13 = 0.33 Ha: p > 0.33The sample proportion was reported to be p̂ = 0.34. Does the value of p exceed one-third by enough to cast substantial doubt on H0?Because the sample size is large, the statisticz = p̂ − 0.33 (0.33)(1 − 0.33)nhas approximately a standard normal distribution when H0 is true. The calculated value of the test statistic isz = 0.34 − 0.33 (0.33)(1 − 0.33)171 = 0.010.036 = 0.28.The probability that a z value at least this inconsistent with H0 would be observed if in fact H0 is true isP−value = P(z ≥ 0.28 when H0 is true) = area under the z curve to the right of 0.28 = 1 − 0.6103 = 0.3897This probability indicates that when p = 0.33, it would not be all that unusual to observe a sample proportion as large as 0.34. When H0 is true, roughly 40% of all samples would have a sample proportion larger than 0.34, so a sample proportion of 0.34 is reasonably consistent with the null hypothesis. Although 0.34 is larger than the hypothesized value of p = 0.33, chance variation from sample to sample is a plausible explanation for what was observed. There is not convincing evidence that the proportion of students who believe that the use of plagiarism-detection software unfairly targets students is greater than one-third.Suppose that the sample proportion was reported to be p = 0.35. Calculate a test statistic (z) for the null hypothesis described in the above example.1.150.56 0.86−0.56Which of the following is NOT true?A P-value is the probability that the H0 is incorrect, given the resulting test statistic.A P-value is a measure of inconsistency between the hypothesized value for a population characteristic and the observed sample. A P-value is the observed level of significance.A P-value is the probability, assuming that H0 is true, of obtaining a test statistic value at least as inconsistent with H0 as what actually resulted.

Given: The sample proportion was reported to be p = 0.35

Answered: Plagiarism is a growing concern among…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Plagiarism is a growing concern among college and university faculty members, and many universities are now using software tools to detect student work that is not original.

An Australian university introduced the use of plagiarism detection software in a number of courses. Researchers surveyed 171 students enrolled in those courses.† In the survey, 58 of the 171 students indicated that they believed that the use of plagiarism-detection software unfairly targeted students.

Assuming it is reasonable to regard the sample as representative of students at this university, does the sample provide convincing evidence that more than one-third of the students at the university believe that the use of plagiarism-detection software unfairly targets students?

With

p = proportion of all students at the university who believe that the use of plagiarism-detection software unfairly targets students

the relevant hypotheses are

H₀: p =

= 0.33

H_a: p > 0.33

The sample proportion was reported to be

p̂ = 0.34.

Does the value of p exceed one-third by enough to cast substantial doubt on H₀?

Because the sample size is large, the statistic

z =

p̂ − 0.33

(0.33)(1 − 0.33)

has approximately a standard normal distribution when H₀ is true. The calculated value of the test statistic is

z =

0.34 − 0.33

(0.33)(1 − 0.33)

171

0.01

0.036

= 0.28.

The probability that a z value at least this inconsistent with H₀ would be observed if in fact H₀ is true is

P−value = P(z ≥ 0.28 when H₀ is true)

= area under the z curve to the right of 0.28

= 1 − 0.6103

= 0.3897

This probability indicates that when

p = 0.33,

it would not be all that unusual to observe a sample proportion as large as 0.34. When H₀ is true, roughly 40% of all samples would have a sample proportion larger than 0.34, so a sample proportion of 0.34 is reasonably consistent with the null hypothesis. Although 0.34 is larger than the hypothesized value of

p = 0.33,

chance variation from sample to sample is a plausible explanation for what was observed. There is not convincing evidence that the proportion of students who believe that the use of plagiarism-detection software unfairly targets students is greater than one-third.

Suppose that the sample proportion was reported to be

p = 0.35.

Calculate a test statistic (z) for the null hypothesis described in the above example.

1.15

0.56

0.86

−0.56

Which of the following is NOT true?

A P-value is the probability that the H₀ is incorrect, given the resulting test statistic.A P-value is a measure of inconsistency between the hypothesized value for a population characteristic and the observed sample. A P-value is the observed level of significance.A P-value is the probability, assuming that H₀ is true, of obtaining a test statistic value at least as inconsistent with H₀ as what actually resulted.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here