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.

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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.

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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

Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.†

(a) If 11 people are called for jury duty, what is the probability that all 11 will be available to serve on the jury? (Round your answer to three decimal places.)


(b) If 11 people are called for jury duty, what is the probability that 5 or more will not be available to serve on the jury? (Round your answer to three decimal places.)


(c) Find the expected number of those available to serve on the jury. What is the standard deviation? (Round your answers to two decimal places.)

(d) How many people n must the jury commissioner contact to be 95.9% sure of finding at least 12 people who are available to serve? (Enter your answer as a whole number.)
people

For patients who have been given a diabetes test, blood-glucose readings are approximately normally distributed with mean 128 mg/dl and a standard deviation 8 mg/dl. Suppose that a sample of 3 patients will be selected and the sample mean blood-glucose level will be computed. Enter answers rounded to three decimal places.

According to the empirical rule, in 95 percent of samples the SAMPLE MEAN blood-glucose level will be between the lower-bound of _________ and the upper-bound of ______

Part 1 Binomial Distribution [Mark 20%/cancer type, 40% total mark]

Five year survival chance from any cancer depends on many factors like availability of treatment options, expertise of attending medical team and more. Five year survival rate is also an important measure and it is used by medical practitioners to report prognosis to patients and family. We will be analyzing five year survival rate of two types of cancer, very aggressive and very treatable cancer and to have comparative analysis of cancer in Norway.

1. Five year survival rate of breast cancer is 87.7%
2. Five year survival rate of esophageal cancer is 16.5%

(NOTE: due to limitation imposed by our available probability distribution table assume survival rate for breast cancer is 90% and for esophageal cancer is 20%)

To simplify our comparative analysis, we will assume 480 patients were admitted in January 2018. For each type of cancer:

1. Calculate the number of patients that are expected to survive at least 5 years, calculate variance and standard deviation expected for 5 year survival.
2. For a selected 15 patients in each category, calculate probability of at least 7 patients surviving past 5 years, compare your calculated value with estimated number from table in page 329. How accurate is our estimation? Do you prefer estimation or calculation methods?
3. Use the table on page 329 of your textbook to determine survival probability for 0 to 15 patients and complete table below.

4. Draw frequency distribution bar graph for each type of cancer
5. What is the minimum/maximum number of survivors expected for given cancer type at 5 years. [HINT: use mean and 3 standard deviations to report outcome].

Part 2 Normal distribution [Mark 30%]

Daily discharge from phosphate mine is normally distributed with a mean daily discharge of 38 mg/L and a standard deviation of 12 mg/L. What proportion of days will the daily discharge exceed 58 mg/L?

Part 3 Normal approximation of binomial Probability Distribution [Mark 30%]

Airlines and hotels often grant reservation in excess to their available capacity, to minimize loss and maximize profitability due to no shows. Suppose that the records of Air Georgian shows that on average, 10% of their prospective passengers will not show up at departure gates. If Air Georgian sells 215 tickets  and their plane has capacity for 200 passengers.

1. Use binomial probability distribution to calculate, the mean of passengers showing up at the gate out of the 215 reservations made
2. Calculate the standard deviation.
3. Calculate standard z score for 200 passengers showing up at the gates.
4. Using normal probability distribution, determine probability of at least 200 passengers will show up!
5. Determine probability of more than 200 passengers showing up at the gate?
6. Determine probability of all 215 passengers showing up at the gate!

n 1998, the Nabisco Company launched a “1000 Chips Challenge” advertising campaign in which it was claimed that every 18-ounce bag of their Chips Ahoy cookies contains 1000 chips (on average). A curious statistics student purchased 8 randomly selected bags of cookies and counted the chocolate chips. The data is given below:

1200 1019 1214 1087 1214 900 1200 825

a) The student concluded that the data was not normally distributed and wanted to use a Wilcoxon Signed-Rank test to test the company’s claim. What assumption is needed in this case?

b) Assuming the assumption in part a. is met, at the 1% significance level, do the data provide sufficient evidence to conclude that the average number of chocolate chips in a bag of Chips Ahoy cookies differs from 1000? Carry out the Wilcoxon Signed-Rank Test by hand.