Past records suggest that the mean annual income,M1, of teachers in state of pennsylvania is less than or equal to the mean annual income,M2, of teachers in Illinois. In a current study, a random sample of 10 teachers from pennsylvania and an independent random sample of 10 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows:

Penn: 37690, 46247, 48701, 34034, 57917, 48242, 50458, 51369, 38914, 47479

Illi: 37791, 39098, 50192, 48432, 38754, 43492, 38217, 53576, 51972, 55200

The population standard deviation for mean annual income of teachers in pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the level 0.01 of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of pennsylvania is less than or equal to the mean annual income of teachers in Illinois? Perform a one-tailed test. Then fill in the table below.

Null hypothesis:

Alternative Hypothesis:

The type of test statistic (plus degrees of freedom if t)

Value of test statistic:

The critical value at the 0.01 level of significance rounded to at least 3 decimal places:

Can we reject the claim that the mean annual income of teachers from pennsylvania is less than or equal to the mean annual income of teachers from illinois?

 

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1. Gain an understanding of the nature of the entity and its industry and then identify

key business risks. After this is completed, assess where the risks of material misstatements could be in the financial report. Consider the factors affecting both

Inherent Risk and Control Risk. Finally, apply the Audit Risk Model [AR = f (IR,

CR, DR)] to the selected company. Which risk rating would you apply (Low, Medium

or High) to the company’s inherent risk assessment and control risk assessment?

How does this affect your assessment of Detection Risk and Audit Risk?

2. Perform analytical procedures of the Statement of Financial Position and of Financial

Performance over the last three years using appropriate ratios and/or metrics. Select

four key ratios and provide a brief explanation in the report. This should be

presented in a table format.

3. Discuss with your group members which account balances are considered “material”.

Explain how you calculated materiality for planning purposes and provide appropriate

justification for your decision-making.

 

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1. Write a brief proposal of the upgrades high lighting the advantages and possible problems

that may be encountered . Highlight legal obligations .

2. Provide realistic running cost savings from new equipment . The hotel has between 20- 30

double guest rooms ( you choose ) provide purchasing and running cost information for new

split system air conditioners and lighits. The old air conditioners are 2 star 3kw units and the

lights at 18 w flurescent tubes, 4 in each room .

3. The swimming pool fences need to be replaced , research legal options , along with

contractors to install fence and resurface the swimming pool . Provide a sustainable option for

pool heating .

4. Source local sustainable suppliers, create new theme and logo for the restaurant

5. Utilise department heads to manage the project , chef , Food and beverage manager and

Front office manager with you being the project manager . Give each department head a

portfolio to manage and clearly outline their responsibilities in redevelopment along with their

KPIs. Ensure you are able to rate their performance against their KPIs as you monitor the

project .

6. Create an interactive Gannt chart that clearly shows departmental roles and allocates tasks to

other staff and contractors as required. Each department must have 4-5 tasks that it is

undertaking, each of these tasks will need to have multiple components ie planning ,

implementation and conclusion and the tasks must be monitored and rated as the progress

against quality , time and budget . Ensure some tasks experienced problems and record

these. Reports must be generated from these results

7. Write a conclusion to this project that outlines how the project was undertaken , the benefits

and the problems encountered . How the project may have been handeled differently . How

the project will help the long term prospects of the hotel .

 

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In the Bayesian graphical model community, the task of inferring which way the arrows point { that is, which nodes are parents, and which children { is one on which much has been written.

Inferring causation is tricky because of `likelihood equivalence”. Two graphical models are likelihood-equivalent if for any setting of the parameters of either, there exists a setting of the parameters of the other such that the two joint probability distributions of all observables are identical. An example ofa pair of likelihood-equivalent models are A ! B and B ! A. The model

A ! B asserts that A is the parent of B, or, in very sloppy terminology, `Accuses B”. An example of a situation where `B ! A” is true is the case whereby is the variable `burglar in house” and A is the variable `alarm is ringing’. Here it is literally true that B causes A. But this choice of words is confusing if applied to another example, R ! D, where R denotes `it rained this morning”

and D denotes `the pavement is dry”. `R causes D” is confusing. I”ll therefore use the words `B is a parent of A” to denote causation. Some statistical methods that use the likelihood alone are unable to use data to distinguish between likelihood-equivalent models. In a Bayesian approach, on the other hand, two likelihood-equivalent models may nevertheless be somewhat distinguished, in the light of data, since likelihood-equivalence does not force a Bayesian to use

priors that assign equivalent densities over the two parameter spaces of the models.

However, many Bayesian graphical modeling folks, perhaps out of sympathy for their non-Bayesian colleagues, or from a latent urge not to appear different from them, deliberately discard this potential advantage of Bayesian methods { the ability to infer causation from data { by skewing their models that the ability goes away; a widespread orthodoxy holds that one should identify the choices of prior for which `prior equivalence” holds, i.e., the priors

such that models that are likelihood-equivalent also have identical posterior probabilities; and then one should use one of those priors in inference and prediction. This argument motivates the use, as the prior over all probability vectors, of specially-constructed Dirichlet distributions. In my view it is a philosophical error to ue only those priors such thatusation cannot be inferred. Priors should be set to describe one”s assumptions; when this is done, it”s likely that interesting inferences about causation can be made from data.

 

 

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