Question

17A national newspaper reported that the state with the longest mean life span is Hawaii, where the population

mean life span is 78 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave the following information about life span (in years) of Honolulu residents.

72 68 81 93 56 19 78 94 83 84

77 69 85 97 75 71 86 47 66 27

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x =  yr

s =  yr

(ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than 78 years? Use a 5% level of significance.

(a) What is the level of significance?

 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student’s t, since we assume that x has a normal distribution and σ is unknown.

The standard normal, since we assume that x has a normal distribution and σ is known.  

The standard normal, since we assume that x has a normal distribution and σ is unknown.

The Student’s t, since we assume that x has a normal distribution and σ is known.

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

19A random sample of 30 binomial trials resulted in 12 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(a) Can a normal distribution be used for the p̂ distribution? Explain. 

Yes, np and nq are both less than 5.

Yes, np and nq are both greater than 5.  

No, np is greater than 5, but nq is less than 5.

No, np and nq are both less than 5.

No, nq is greater than 5, but np is less than 5.

(c) Compute p̂. 

 

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Question

pounds. Suppose that last summer 62 out of a random sample of 85 guests did, in fact, catch northern pike weighing

over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use α = 0.05.

(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.)

25. Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing in Computer Studies of the Humanities and Verbal Behavior (Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato’s Republic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato’s time (about 427 – 347 B.C.). A random sample of 312 five-syllable sequences from the newly discovered manuscript showed that 60 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato’s Republic? 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.)

 

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