How would you interpret a correlation coefficient of -0.95 between the two parameters; age of the patient and the testosterone level? How would your interpretation change if the coefficient was 0.03 or 0.48?

Please provide solutions to the following problems. Please use Excel to solve the problems and submit the Excel spreadsheet.

2. You started a new restaurant. Based on invoices for the first 30 days, you estimated your average grocery bill to be $20,000 with a standard deviation of $2000. You want to start another restaurant in a similar neighborhood and you are planning to prepare a brochure for investors and to work out a deal with a whole sale food distributor. Prepare a 95% confidence interval for the average grocery bill. Would a 99% confidence interval be narrower or wider than the 95% confidence interval?

Stratified Sampling and Cluster Sampling are two approaches used within Probability Sampling Techniques.

Explain using examples, instances where Stratified Sampling would be preferred over Cluster Sampling, and vice versa.

Remember to cite your source using current APA format, and post the url for your paper. Your original post should be no more than 250 words.

A city council suspects a judge of being a "hanging judge" because s/he is perceived as imposing harsher penalties for the same sentence. To investigate this, a random sample of 47 cases is taken from the judge's prior cases that resulted in a guilty verdict for a certain crime. The average jail sentence s/he imposed for the sample is 26 months. The average jail sentence for the same type of crimes is 25 months with a standard deviation of 13 months. What can be concluded with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- cases same type of crimes city council judge's prior cases months
Sample:
---Select--- cases same type of crimes city council judge's prior cases months

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

For the same sentence, the judge imposed significantly harsher penalties than other judges.

For the same sentence, the judge imposed significantly milder penalties than other judges.   

For the same sentence, the judge's penalties did not significantly differ from other judges.

Please solve the following questions. Please show all work and all steps.

1a.) Find CDF of the Bernoulli Distribution.

1b.) Explain your reasoning for part 1a above. Do not use a series result.

2a.) For the geometric distribution, show that the geometric pdf is actually a pdf (all probabilities are greater than or equal to 0 and the sum of the pdf from x=1 to x=infinity is equal to 1).

2b.) Find E(X) for 2a above.

2c.) Find V(X) for 2a above.

Suppose a geyser has a mean time between eruptions of 80 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 26 minutes​, answer the following questions. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 92 ​minutes? The probability that a randomly selected time interval is longer than 92 minutes is approximately 0.3228. ​(Round to four decimal places as​ needed.) ​(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 92 ​minutes? The probability that the mean of a random sample of 8 time intervals is more than 92 minutes is approximately nothing. ​(Round to four decimal places as​ needed.)

ONLY ANSWER PART B

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care):

57.2 56.1 53.1 65.8 59.0 64.7 70.1 64.7 53.5 78.2

Assume that the population of x values has an approximately normal distribution.

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.)

x = %

s = %

(b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.)

lower limit %

upper limit %

consider the linear programming problem

maximize z = x1 +x2

subjected tp

x1 + 3x2 >= 15

2x1 + x2 >= 10

x1 + 2x2 <=40

3x1 + x2 <= 60

x1 >= 0, x2>= 0

solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. Upon analyzing the results, you find that the correlation coefficient has a value of −0.25. On the basis of this data, respond to the following:

• How would you interpret the correlation coefficient in terms of strength and direction?
• How would the results be affected if you increased the number of subjects in the study to one thousand? Why might that affect the overall correlation?
• How important is it to randomly select subjects? Explain in detail using an example of a sample that might not be truly representative of the population.

Write up a short paragraph in your own words, describing what Baye's Theorem is and how is it related to Conditional Probability and the Multiplication Rule. Base on the research, determine what the second fraction would be.

1.14 Let Xn be a Markov chain on state space {1,2,3,4,5} with transition matrix

P=

(a) Is this chain irreducible? Is it aperiodic?

(b) Find the stationary probability vector.

The Army finds that the head sizes (forehead circumference) of soldiers has a normal distribution with a mean of 22.7 inches and a standard deviation of 1.1 inches.

1. Approximately 68% of soldiers have head sizes between (, ) inches.
2. Approximately 95% of soldiers have head sizes between (, ) inches.
3. Approximately 99.7% of soldiers have head sizes between (, ) inches.

What is a dummy variable? If we use one on the right-hand side of the equation in a multivariate analysis, what are the implications for interpreting the constant?  What is multicollinearity? How do we know if we have it in our models? How do we correct for it if we do?  What is hetereskedasticity? Should we really be concerned about it? Why or why not?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. Here are data on the "penetrability" of the same type of soil at two levels of compression. Penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil.

Compressed Soil

Intermediate Soil

Use the data, omitting the high outlier, to give a 96% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. Compute degrees of freedom using the conservative method.

In your opinion, which calculation is more informative to a primary care physician in a rural village—incidence rates or prevalence rates of HIV? Explain your answer and provide an example to support your response.