Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009.† These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by 40% or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in an Asian city showed a mean of $1,118 per square meter with a standard deviation of $230. Annual lease rates for a sample of 40 commercial properties in a European city showed a mean lease rate of $987per square meter with a standard deviation of $195.

b) what is the value of the test statistic? (round your answer to three decimal places)

c) what is the p-value? (round your answer to four decimal places.)

Chi Square Test

We will now use Excel to run an example of a chi square test. Chi square test is checking the independence of two variables. Our example will test if taking hormonal pills and being overweight are related. We will test the independence on 200 random patients. Thus, N=200. They will be divided first into two groups, those who take hormonal pills and those who do not. Second, they will be divided into three groups based on weight, not overweight, overweight and obese. All data is in this table
Observed frequency table   Not overweight   overweight   obese   total
Not taking hormonal pills   35 36 49   120
Take hormonal pills 33 32 15   80
Total 68 68 64   200

We will start in Excel by making the above table in region A1-E4, first five columns and first four rows. That is, in celll B1 you will type Not overweight, in cell A2 Not taking hormonal pills, etc
Next we construct the expected table. Let's make it in the region A8-E11. Type Expected frequency table in cell A8, not overweight in cell B8 etc. Data in the table is calculated in this fashion. Cell B10 corresponds to the take hormonal pills row and not overweight column. Thus in cell B10 we type =B4*E3/E4. In cell D10 we type =D4*E3/E4. Using that strategy complete the expected frequency table.
Next we check if chi square test will work for this example. When you remove total from the expected frequency table, you have a 2x3 table with 6 entries. To run chi square we should first have no zero entries out of those 6. In cell A13 type zero entries. In cell B13 type the actual value of how many zero entries you have in expected frequency table. Second, you should have at most 20% entries that are less than 5. In cell A14 type percentage of entries less than 5. In cell B14 calculate the actual value of percents of entries in expected frequency table that are less than 5.
Now let's evaluate chi square parameters. In cell A16 type df. In cell B16 evaluate df. In cell A20 type chi square. We will evaluate chi square in cell B20. In cell B20 type =(B2-B9)^2/B9+(B3-B10)^2/B10+(C2-C9)^2/C9+(C3-C10)^2/C10+(D2-D9)^2/D9+(D3-D10)^2/D10. In cell A22 type table chi square and then find the table value on page 416 with .05 level of significance and degrees of freedom df from B16. Put that value in cell B22.
Now we do testing. In cell A24 type H0 and in cell B24 state the null hypothesis. In cell A25 type H1 and in cell B25 state the alternate hypothesis.
Now compare the values in cells B20 and B22. State if we reject or do not reject the null hypothesis in cell A26. Explain how you obtained your conclusion in cell B26.

Next we will test it another way, with asymptotic significance (probability).
In cell A28 type Asymp. Sig. (probability). We will evaluate Sig. in cell B28. We will use an Excel command for finding sig. in a chi square test. In cell B28 type =CHITEST(B2:D3,B9:D10).
Compare the sig. in cell B28 with the significance level of .05 and using that comparison, state in cell A31 if we reject or do not reject the null hypothesis. Explain how you have reached your statement in cell B31.

Is 2k-1 odd?
I get that 2(some int k) + 1 is the property for odd numbers.
The main question:
I am confused on how 2k-1= 2k-2+1 which is a form of k?

1. weight vs. age α ̇=.01/2

Step 1:                       Ho:    __   _   ___

                                   Ha:    __   _ ___

Step 2:                       Alpha level = _____

Step 3:           Sampling distribution is df = _____

Step 4:           Decision Rule: I will reject the Ho if the |_robs_| value falls at or beyond
                          the |_rcrit_| of ____, otherwise I will fail to reject

Step 5:           Calculation: \_robs_/ = _____

Step 6:           Summary: Since the |_robs_| of ____     _____________ the |_rcrit_| of

                       _____, I therefore reject/fail to reject (choose one) the Ho.

Step 7:           Conclusion: Since _______ occurred, I conclude ___________________________________________________________________.

2. height vs. shoe size α ̇=.02/2

Step 1:                       Ho:    __   _   ___
                                   Ha:    __   _ ___

Step 2:                       Alpha level = _____

Step 3:           Sampling distribution is df = _____

Step 4:           Decision Rule: I will reject the Ho if the |_robs_| value falls at or beyond
                          the |_rcrit_| of ____, otherwise I will fail to reject

Step 5:           Calculation: \_robs_/ = _____

Step 6:           Summary: Since the |_robs_| of ____     _____________ the |_rcrit_| of

                       _____, I therefore reject/fail to reject (choose one) the Ho.

Step 7:           Conclusion: Since _______ occurred, I conclude ___________________________________________________________________.

3.Explain the correlation coefficient of determination.

Match each example to the type of bias that would result

3. Load the dataset called ec122a.csv and decide the appropriate regression to run. Write down what transformations, corrections, etc... you make and why.

please show all work

A travel agent wants to estimate the proportion of vacationers who plan to travel outside the United States in the next 12 months. A random sample of 130 vacationers revealed that 40 had plans for foreign travel in that time frame. Construct a 95% confidence interval estimate of the population proportion. Make a statement about this in context of the problem

The number of goods sold by “The Local” is in excess of one million per year with deliveries being about 40% of that figure. The amount of goods sold has decreased marginally in recent years. “The Local” is wholly owned but Bianca and her staff have a standard of living to maintain so there is some pressure to raise overall sales whilst keeping costs, particularly delivery costs, in check.     Bianca continues: It is your job to use the sample data from last year’s overall sales to do some statistical analyses and interpretations, investigating what the current overall sales of the business are and providing insights that will guide future business decisions.

Below is last years overall sales vs deliveries data.

1. Please identify the qualitative and quantitative discrete, continuous varibles?

2. Is it cross sectional or time series data?

3. How do you calculate z scores and which are outliers?

4. How do you calculate the covariance and correlation and what does it mean?

The table shows the results of a survey in which 142 men and 145 woman workers age 25 to 64 were asked if they have at least one months income set aside for emergencies. Complete parts a-d. a.) Find the probability that a randomly selected worker has one months income or more set aside for emergencies. b.) Given that a randomly selected worker is male find the probability that the worker has less than one months income. c.) Given that a randomly selected woker has one months income or more, find the probablitly that the worker is female. d.) Are the events "having less than one months income saved" and "being male" independant?

Researchers for an advertising company are interested in determining if people are more likely to spend more money on beer if advertisers put more beer ads on billboards in a neighborhood in Philadelphia. They estimate that 250 people will view their billboard in one week. They determine that the total number of residents in the neighborhood is 600. So, the residents who have not viewed the billboard are in the control group. The researchers determine that those who did view the ads spent $24 per week on beer and those who did not view the ads spent $16 per week on beer.

1. Calculate the treatment effect.

2. Calculate the standard error (hint: the researchers determined the Std. Dev. for the control is $1.3 and the Std. Dev. for the treatment is $0.90)

3. Calculate the t-statistic.

4. Can we reject OR fail to reject the null hypothesis? Explain why.

SELECT a simple random sample size 37 from the cereal data. Outline in detail the process you used and identify the fist 4 members of your example.

- Use the variable Mfr for this sample of 37 to answer each of the following.

(a). identify the variable of interest along with the level of measure.

(b) CONSTRUCT a frequency table for the data.

(c) Display the data in a graph. Be sure to include all the proper labels in the graph.

(d) describe the shape of the data if it is appropiate to do so. If it is not appropiate to describe the shape then explain why.

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer.

Use a 5% level of significance to test the claim that the natural distribution of browse fits the deer feeding pattern.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are different.

H₁: The distributions are the same.    

H₀: The distributions are the same.

H₁: The distributions are the same.

H₀: The distributions are the same.

H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

chi-square

binomial    

normal

uniform

Student's t

What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the natural distribution of browse does not fit the feeding pattern.

At the 5% level of significance, the evidence is insufficient to conclude that the natural distribution of browse does not fit the feeding pattern

Problem 6.
1. If X N(9; 4), nd Pr(jX ? 2j < 4).
2. If X N(0; 1), nd Pr(jX + 3j > 5).
3. If X N(?2; 9), nd the number c such that Pr(jX + 2j < c) = 0:5.

A device is used in many kinds of systems. Assume that all systems have either 1, 2, 3, or 4 of these devices and that each of these four possibilties is equally likely to be the case. Each device in a system has probablility = 0.1 of failing, and the devices function independently of one another. This implies that once we know how many devices are present, the probability distribution of the number of failures will be known. E.g. if a system employs 3 of the devices, then the number that fail will have a binomial distribution with parameters n = 3 and p = 0.1

Denote with X, the number of failures of devices in the system, and with Y, the total number of devices in the system. What is observed is that for b = 1,2,3, and 4, the conditional probability mass function is the binomial probability mass function with parameters n = b, and p = 0.1

a) Find the joint probability mass table of P(X,Y)