Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leacht 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 Achens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 131 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 a- 0.01. A USE SALT (a) what is the level of significance? State the null and alternate hypotheses. Hip< 0.214; H,1p = 0.214 Hip> 0.214; H, 1p = 0.214 HIp= 0.214; H, p< 0.214 Hi p = 0.214; H,: p = 0.214 • DH,:p- 0.214; H,1 p> 0.214 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5. O The Student'sE, since np < 5 and ng < 5. O The Student'st, since np > 5 and ng > 5. • The standard normal, since np > 5 and ng > 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.)

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Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leacht 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 498 five-syllable sequences from this manuscript showed that 131 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 a = 0.01.
A USE SALT
(a) what is the level of significance?
State the null and alternate hypotheses.
H.p< 0.214; H,:p = 0.214
H: p> 0.214; H,:p = 0.214
Hip= 0.214; H, :p < 0.214
H,ip = 0.214; H,:p+ 0.214
O DH, p = 0.214; H,: p> 0.214
(b) What sampling distribution will you use?
O The standard normal, since np < 5 and ng < 5.
O The Student's t, since np << 5 and ng < 5.
O The Student's t, since np > 5 and ng > 5.
• The standard normal, since np > 5 and ng > 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 ansvwer to four decimal places.)
Transcribed Image Text:Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leacht 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 498 five-syllable sequences from this manuscript showed that 131 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 a = 0.01. A USE SALT (a) what is the level of significance? State the null and alternate hypotheses. H.p< 0.214; H,:p = 0.214 H: p> 0.214; H,:p = 0.214 Hip= 0.214; H, :p < 0.214 H,ip = 0.214; H,:p+ 0.214 O DH, p = 0.214; H,: p> 0.214 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5. O The Student's t, since np << 5 and ng < 5. O The Student's t, since np > 5 and ng > 5. • The standard normal, since np > 5 and ng > 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 ansvwer to four decimal places.)
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