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 311 five syllable sequences from the newly discovered manuscript showed that 60 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 0 01 (a) What is the level of significance State the null and alternate hypotheses H 0 p 0 261 H 1 p 0 261 H 0 p 0 261 H 1 p 0 261 H 0 p 0 261 H 1 p 0 261 H 0 p 0 261 H 1 p 0 261 (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 (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 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

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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

Syllables were categorized as long or short. On analyzing Plato'sRepublic, 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 of311five-syllable sequences from the newly discovered manuscript showed that60are 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'sRepublic? Use= 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:p0.261;H₁:p= 0.261

H₀:p= 0.261;H₁:p0.261

(b) What sampling distribution will you use?

The standard normal, sincenp< 5 andnq< 5.

The Student'st, sincenp> 5 andnq> 5.

The Student'st, sincenp< 5 andnq< 5.

The standard normal, sincenp> 5 andnq> 5.

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

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

(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 differs from that of the text of Plato'sRepublic.

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'sRepublic.