Suppose you want to test the claim that a population mean equals 46.(

a)State the null hypothesis. H₀: > 46H₀: < 46 H₀: = 46H₀: 46H₀: 46

(b)State the alternate hypothesis if you have no information regarding how the population mean might differ from 46. H₁: > 46H₁: < 46 H₁: = 46H₁: 46H₁: 46

(c)State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may exceed 46. H₁: > 46H₁: < 46 H₁: = 46H₁: 46H₁: 46

(d)State the alternative hypothesis if you believe (based on experience or past studies) that the population mean may be less than 46. H₁: > 46H₁: < 46 H₁: = 46H₁: 46H₁: 46

Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=2.9%.A random sample of10 bankstocks gave the following yields (in percents).

• 5.7
• 4.8
• 6.0
• 4.9
• 4.0
• 3.4
• 6.5
• 7.1
• 5.3
• 6.1

The sample mean is= 5.38%. Suppose that for the entire stock market, the mean dividend yield is=4.5%.Do these data indicate that the dividend yield of all bank stocks is higher than4.5%? Use=0.01. (a)

What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:= 4.5%;H₁:4.5%; two-tailedH₀:>4.5%;H₁:= 4.5%; right-tailed H₀:= 4.5%;H₁:<4.5%; left-tailedH₀:= 4.5%;H₁:>4.5%; right-tailed

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume thatxhas a normal distribution with unknown.The standard normal, since we assume thatxhas a normal distribution with known. The Student'st, since we assume thatxhas a normal distribution with known.The Student'st, sincenis large with unknown.

Compute thezvalue of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c)

Find (or estimate) theP-value. (Enter a number. Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value. (Select the correct graph.)

(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)

State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.

3.

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). (Reference: Hummingbirds, K. Long, W. Alther.) Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean is= 3.75 grams. Letxbe a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume thatxhas a normal distribution and=0.64gram.Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is=4.30grams.Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than4.30grams?Use=0.10.(a)

What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H₀:= 4.3 g;H₁:> 4.3 g; right-tailedH₀:= 4.3 g;H₁:4.3 g; two-tailed H₀:< 4.3 g;H₁:= 4.3 g; left-tailedH₀:= 4.3 g;H₁:< 4.3 g; left-tailed

(b)

What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume thatxhas a normal distribution with known.The standard normal, since we assume thatxhas a normal distribution with unknown. The Student'st, since we assume thatxhas a normal distribution with known.The Student'st, sincenis large with unknown.

Compute thezvalue of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c)

Find (or estimate) theP-value. (Enter a number. Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value. (Select the correct graph.)

(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= 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e)

State your conclusion in the context of the application. There is sufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than4.30 grams.There is insufficient evidence at the 0.10 level to conclude that humming birds in the Grand Canyon weigh less than4.30 grams.

4.

A random sample of20binomial trials resulted in8successes. 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 thedistribution? Explain. No,npis greater than 5, butnqis less than 5.No,npandnqare both less than 5. No,nqis greater than 5, butnpis less than 5.Yes,npandnqare both greater than 5.Yes,npandnqare both less than 5.

(b)

State the hypotheses. H₀:p= 0.5;H₁:p<0.5H₀:p<0.5;H₁:p= 0.5 H₀:p= 0.5;H₁:p>0.5H₀:p= 0.5;H₁:p0.5

(c)

Compute. (Enter a number.) p hat = Compute the corresponding standardized sample test statistic. (Enter a number. Round your answer to two decimal places.) (d)

Find theP-value of the test statistic. (Enter a number. Round your answer to four decimal places.) (e)

Do you reject or fail to rejectH₀? Explain. At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(f)

What do the results tell you? The samplevalue based on 20 trials is sufficiently different from 0.50 to not rejectH₀for= 0.05.The samplevalue based on 20 trials is not sufficiently different from 0.50 to justify rejectingH₀for= 0.05. The samplevalue based on 20 trials is not sufficiently different from 0.50 to not rejectH₀for= 0.05.The samplevalue based on 20 trials is sufficiently different from 0.50 to justify rejectingH₀for= 0.05.

5. 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 inComputer Studies of the Humanities and Verbal Behavior(Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato'sRepublic, 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 of317five-syllable sequences from the newly discovered manuscript showed that61are 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'sRepublic? Use= 0.01.(a)

What is the level of significance? State the null and alternate hypotheses. H₀:p= 0.261;H₁:p0.261H₀:p= 0.261;H₁:p> 0.261 H₀:p0.261;H₁:p= 0.261H₀:p= 0.261;H₁:p< 0.261

(b)

What sampling distribution will you use? The standard normal, sincenp> 5 andnq> 5.The standard normal, sincenp< 5 andnq< 5. The Student'st, 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. (Select the correct graph.)

(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 application. There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato'sRepublic.There is insufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato'sRepublic.