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Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text.
Computer Studies of the Humanities and Verbal BehaviorRepublic32062Republicα = 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 np > 5 and nq > 5.
The Student's t, since np > 5 and nq > 5.
The standard normal, since np < 5 and nq < 5.
The Student's t, 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 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.
