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 481 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 α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 0.214; H1: p > 0.214 H0: p < 0.214; H1: p = 0.214 H0: p = 0.214; H1: p ≠ 0.214 H0: p = 0.214; H1: p < 0.214 H0: 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 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. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 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.

Answer 1

(a) Option: H₀: p = 0.214; H₁: p >0.214

(b) n=481, Under H₀, np=481*0.214=102.934>5, nq=n(1-p)=481*(1-0.214)=378.066>5 so assumption of normality holds and we use Z test.

Option: The standard normal, since np > 5 and nq > 5.

(d) Since P-value<0.01,

Option: 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 is higher than that in Plato's Symposium.