Question

Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This...

Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of 317 five-syllable sequences from the newly discovered manuscript showed that 61 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato's Republic? Use α = 0.01.

(a) What is the level of significance? ________

State the null and alternate hypotheses.

___H0: p ≠ 0.261; H1: p = 0.261

___H0: p = 0.261; H1: p ≠ 0.261     

___H0: p = 0.261; H1:  p > 0.261

___H0: p = 0.261; H1:  p < 0.261

(b) What sampling distribution will you use?

___The standard normal, since n·p > 5 and n·q > 5.

___The standard normal, since n·p < 5 and n·q < 5.     

___The Student's t, since n·p < 5 and n·q < 5.

___The Student's t, since n·p > 5 and n·q > 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.) ______

(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 α?

___At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

___At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

___At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

___At the α = 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 differs from that of the text of Plato's Republic.

___There is insufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato's Republic.    

Homework Answers

Answer #1

a)

H0: p = 0.261; H1: p ≠ 0.261   

b)
The standard normal, since n·p > 5 and n·q > 5.

c)


phat = 61/317 = 0.192


z = (phat - p)/sqrt(p*(1-p)/n)
= (0.192 - 0.261)/sqrt(0.261*(1-0.261)/317)
= -2.80

c)

p value = 0.0052

d)

_At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

e)

There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato's Republic.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This...
Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about...
Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This...
Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato's Republic, Wishart and Leach found that about...
Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found...
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 481 five-syllable sequences from this manuscript showed that 125 were of the type four short and one long. Do...
A random sample of 30 binomial trials resulted in 12 successes. Test the claim that the...
A random sample of 30 binomial trials resulted in 12 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the  distribution? Explain. Yes, n·p and n·q are both greater than 5 .No, n·p and n·q are both less than 5.     Yes, n·p and n·q are both less than 5 .No, n·p is greater than 5, but n·q is less than 5....
A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the...
A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p hat distribution? Explain. No, n·p and n·q are both less than 5. No, n·p is greater than 5, but n·q is less than 5. No, n·q is greater than 5, but n·p is less than 5. Yes, n·p and...
a) USA Today reported that about 47% of the general consumer population in the United States...
a) USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1002 Chevrolet owners and found that 482 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01. What is the T value and the P Value? Wishart and Leach...
Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found...
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 499 five-syllable sequences from this manuscript showed that 132 were of the type four short and one long. Do...
Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found...
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 500 five-syllable sequences from this manuscript showed that 131 were of the type four short and one long. Do...
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the...
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 19 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 0.67; H1: p ≠...
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the...
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 40 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 0.67; H1: p >...