#9

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 of499five-syllable sequences from this manuscript showed that132were 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?

State the null and alternate hypotheses.

H₀:p< 0.214;H₁:p= 0.214

H₀:p= 0.214;H₁:p0.214

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 Student'st, sincenp> 5 andnq> 5.

The standard normal, sincenp< 5 andnq< 5.

The standard normal, sincenp> 5 andnq> 5.

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

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

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

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