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 of482five-syllable sequences from this manuscript showed that127were 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< 0.214H₀:p= 0.214;H₁:p0.214 H₀:p> 0.214;H₁:p= 0.214H₀:p< 0.214;H₁:p= 0.214H₀:p= 0.214;H₁:p> 0.214

(b)What sampling distribution will you use?

The Student'st, sincenp> 5 andnq> 5.The Student'st, sincenp< 5 andnq< 5. The standard normal, 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.)(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.

A plot of the standard distribution curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.65 is shaded.

A plot of the standard distribution curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 2.65 and 4 is shaded.

A plot of the standard distribution curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and 1.65 is shaded.

A plot of the standard distribution curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.65 as well as the area under the curve between 1.65 and 4 are both shaded.

(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 applicati