(1) 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 488 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? _________

(b) 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.) ________

(2) 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 316 five-syllable sequences from the newly discovered manuscript showed that 61 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? _____________

(b) 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.)

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.

3. Take the mean and standard deviation of data set A calculated in problem 1 and assume that they are population parameters (μ and σ) known for the variable fish length in a population of rainbow trouts in the Coldwater River. Imagine that data set B is a sample obtained from a different population in Red River (Chapter 6 problem!). a) Conduct a hypothesis test to see if the mean fish length in the Red River population is different from the population in Coldwater River. b) Conduct a hypothesis test to see if the variance in fish length is different in the Red River population compared to the variance in the Coldwater population.

• Data set A: total= 677.98, mean= 67.798, n= 10, variance= 0.663084, std devition= 0.814299972

• Data set B: total= 574.24, mean=71.78, n=8, variance= 0.727143, std devition= 0.852726719

 Do not use excel function for p value.  Show all your work

QUESTION 7

1. The Federal Reserve Board of Governors recently changed the reporting of its stance on monetary policy from what they termed a "policy bias" to a "balance of risks". A researcher wished to see whether there had been a change in the way financial analysts were interpreting the change in reporting. When the "policy bias" reporting method was used, it was known that only 35% of the Board's decisions were correctly anticipated by analysts in their reports. For the "balance of risks" method, the researcher took a random sample of 56 analysts' reports and found that 26 of these correctly anticipated the Board's decision. Assume that the test is to be carried out at the 10% level.

   1. State the direction of the alternative hypothesis used to test whether the proportion of analysts correctly anticipating the Board's decision had changed. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
   2. Calculate the test statistic, reporting your answer to two decimal places.
   3. Use the tables in the textbook to determine the p-value for the test (answer to 4 decimal places)
   4. Is the null hypothesis rejected for this test? Type yes or no.
   5. Disregarding your answer for 4, if the null hypothesis was rejected at the 10% level, would the predictive accuracy of the claims in analysts' reports appear to have changed under the new system? Type yes or no.

Refer to the Baseball 2016 data, which reports information on the 2016 Major League Baseball season. Let attendance be the dependent variable and total team salary be the independent variable. Determine the regression equation and answer the following questions.

Draw a scatter diagram. From the diagram, does there seem to be a direct relationship between the two variables?

What is the expected attendance for a team with a salary of $100.0 million?

If the owners pay an additional $30 million, how many more people could they expect to attend?

At the .05 significance level, can we conclude that the slope of the regression line is positive? Conduct the appropriate test of hypothesis.

What percentage of the variation in attendance is accounted for by salary?

Determine the correlation between attendance and team batting average and between attendance and team ERA. Which is stronger? Conduct an appropriate test of hypothesis for each set of variables.

Show all work in Excel

Carleton Chemical claims that they can produce an average of more than 800 tons of meladone
per week. A random sample of 36 weeks of production yielded a sample mean of 823 tons, with
a standard deviation of 79.8 tons.

Does the sample data provide sufficient evidence to support the claim
made by Carleton Chemical?   Use a significance level of α = .05.

1. What is the z-score associated with the 75th percentile?

2. What z-scores bound the middle 50% of a normal distribution?

3. What z-score has 10% of the distribution above it?

4. What z-score has 20% of the distribution below it?

5. Reading comprehension scores for junior high students are normally distributed with a mean of80.0 and a standard deviation of 5.0.
a. What percent of students have scores greater than 87.5?

b. What percent of students have scores between 75 and 85

The New Jersey Department of Public Health offers psychological support programs for substance abuse patients with depression. It is suggested that the type of depression varies by the type of substance abuse. If so, such a relationship might help the department better target treatments. They random sample 75 medically declared substance abusers with depression. (C15PROB7.SAV) (χ2 = 5.12, p=.077; V=0.26; Lambdarow= 0.11, p > .05

Select and justify the best test(s). The chi-square, Phi, Yates, or Lambda (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.

 Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.

 Do the math and reject/retain null at a=.05. State your critical value.

 Explain the results in plain language.

A researcher wishes to determine whether there is a significant relationship between the gender of psychology students and the refreshment drink they prefer. The results obtained from a survey of students are presented in the following table: Preferred Drink Gender Water Coffee Soda Total Male 46 29 40 115 Female 29 36 70 135 Total 75 65 110 250.

Perform an appropriate two-tailed hypothesis test at α = 0.05. If a significant result is obtained, determine the strength of the relationship. Show all four decision making steps. (20)

Determine the sample size n needed to construct a 90​% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 8​%.

a. p over bar equals 0.10

b. p over bar equals 0.20

c. p over bar equals 0.30

Click the icon to view a table of standard normal cumulative probabilities.

At a university the historical mean of scholarship examination scores for freshman applications is 800. A historical population standard deviation  σ = 150 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

(a) State the hypotheses.

(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 90 applications provided a sample mean x = 834?

(c) Use the confidence interval to conduct a hypothesis test. Using  α = 0.05,  what is your conclusion?

(d) What is the test statistic? What is the p-value?

Refer to the Lincolnville School District bus data.

Conduct a test of hypothesis to reveal whether the mean maintenance cost is equal for each of the bus manufacturers. Use the .01 significance level.

Conduct a test of hypothesis to determine whether the mean miles traveled since the last maintenance is equal for each bus manufacturer. Use the .05 significance level.

Show work in Excel.

The dataset TrafficFlow gives the delay time in seconds for 24 simulation runs in Dresden, Germany, comparing the current timed traffic light system on each run to a proposed flexible traffic light system in which lights communicate traffic flow information to neighboring lights. On average, public transportation was delayed 105 seconds under the timed system and 44 seconds under the flexible system. Since this is a matched pairs experiment, we are interested in the difference in times between the two methods for each of the 24 simulations. For the n=24 differences D, we were given that x¯D=61 seconds with sD=15.19 seconds. We wish to estimate the average time savings for public transportation on this stretch of road if the city of Dresden moves to the new system.

what parameter are we estimating? give correct notation

suppose that we write the 24 differences on 24 slips of paper. describe how to physically use the paper slips to create a bootstrap sample.

what statistic do we for this one bootstrap sample?

if we create a bootstrap distribution using many of these bootstrap statistics what shape do we expect it to be centered?

how can we use the values in the bootstrap distribution to find the standard error?

the standard error 3.1 for one set of 10,000 bootstrap samples. find and interpret a 95% confidence interval for the average time savings.

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H₀: μ = 30

H_a: μ ≠ 30

The population standard deviation is 14. Use  α = 0.05. How large a sample should be taken if the researcher is willing to accept a 0.10 probability of making a type II error when the actual population mean is 34?

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean? 0.50 equal to the probability of selecting a sample mean that is at most equal to the population mean all of the above none of the above