Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 480 five-syllable sequences from this manuscript showed that 125 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use ? = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: p > 0.214; H1: p = 0.214H0: p = 0.214; H1: p > 0.214 H0: p = 0.214; H1: p ≠ 0.214H0: p < 0.214; H1: p = 0.214H0: p = 0.214; H1: p < 0.214 (b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5. The Student's t, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −1.48 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and 1.48 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.48 and 4 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −1.48 as well as the area under the curve between 1.48 and 4 are both shaded.

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 480 five-syllable sequences from this manuscript showed that 125 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use ? = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: p > 0.214; H1: p = 0.214H0: p = 0.214; H1: p > 0.214 H0: p = 0.214; H1: p ≠ 0.214H0: p < 0.214; H1: p = 0.214H0: p = 0.214; H1: p < 0.214 (b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5. The Student's t, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −1.48 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and 1.48 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.48 and 4 is shaded. A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −1.48 as well as the area under the curve between 1.48 and 4 are both shaded.

Name: Symposium is part of a larger work referred to as Plato's Dialogues. W
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has

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

Concept explainers

Topic Video

Question

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 480 five-syllable sequences from this manuscript showed that 125 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use ? = 0.01.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀: p > 0.214; H₁: p = 0.214H₀: p = 0.214; H₁: p > 0.214 H₀: p = 0.214; H₁: p ≠ 0.214H₀: p < 0.214; H₁: p = 0.214H₀: p = 0.214; H₁: p < 0.214

(b)

What sampling distribution will you use?

The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5. The Student's t, since np > 5 and nq > 5.The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)

Find the P-value of the test statistic. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

A plot of the standard distribution curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −1.48 is shaded.

(d)

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence is higher than that in Plato's Symposium.There is insufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence is higher than that in Plato's Symposium.

Expert Solution

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Sample space, Events, and Basic Rules of Probability$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.