Symposiumis part of a larger work referred to as Plato'sDialogues. Wishart and Leachfound that about 21.4% of five-syllable sequences inSymposiumare 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'sDialogues. A random sample of496five-syllable sequences from this manuscript showed that131were 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'sSymposium? Use= 0.01.

(a) What is the level of significance?

(b) 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:p0.214

(c)What sampling distribution will you use?

• 1. The standard normal, sincenp< 5 andnq< 5.
• 2. The Student'st, sincenp< 5 andnq< 5.
• 3. The Student'st, sincenp> 5 andnq> 5.
• 4. The standard normal, sincenp> 5 andnq> 5.

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

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

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

(g) 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?

• 1. At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
• 2. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
• 3. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• 4. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(h)Interpret your conclusion in the context of the application.

• 1. 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'sSymposium.
• 2. 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'sSymposium.