Question #1
A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.
(c) Compute p̂.
Compute the corresponding standardized sample test statistic.
(Round your answer to two decimal places.)
(d) Find the P-value of the test statistic. (Round your
answer to four decimal places.)
Question # 2
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 491 five-syllable sequences from this manuscript showed that 128 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?
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.
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