8. Given the following data: Number of patients = 3,293 Number of patients who had a positive test result and had the disease = 2,184 Number of patients who had a negative test, and did not have the disease = 997 Number of patients who had a positive test result, but did not have the disease = 55 Number of patients who had a negative test result, but who had the disease = 57 a. Create a complete and fully labeled 2x2 table (10) b. Calculate the positive predictive value (5) c. Calculate the negative predictive value (5) d. Calculate the likelihood ratio for a positive test result (5) e. Calculate the likelihood ratio for a negative test result (5)

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Jan Northcutt, owner of Northcutt Bikes, started business in 1995. She notices the quality of bikes she purchased for sale in her bike shop declining while the prices went up. She also found it more difficult to obtain the features she wanted on ordered bikes without waiting for months. Her frustration turned to a determination to build her own bikes to her particular customer specifications.

She began by buying all the necessary parts (frames, seats, tires, etc.) and assembling them in a rented garage using two helpers. As the word spread about her shop’s responsiveness to options, delivery, and quality, however, the individual customer base grew to include other bike shops in the area. As her business grew and demanded more of her attention, she soon found it necessary to sell the bike shop itself and concentrate on the production of bikes from a fairly large leased factory space.

As the business continued to grow, she backward integrated more and more processes into her operation, so that now she purchases less than 50% of the component value of the manufactured bikes. This not only improves her control of production quality but also helps her control the costs of production and makes the final product more cost attractive to her customers.

The Current Situation

Jan considers herself a hands-on manager and has typically used her intuition and her knowledge of the market to anticipate production needs. Since one of her founding principles was rapid and reliable delivery to customer specification, she felt she needed to begin production of the basic parts for each particular style of bike well in advance of demand. In that way she could have the basic frame, wheels, and standard accessories started in production prior to the recognition of actual demand, leaving only the optional add-ons to assemble once the order came in. Her turnaround time for an order of less than half the industry average is considered a major strategic advantage, and she feels it is vital for her to maintain or even improve on response time if she is to maintain her successful operation.

As the customer base have grown, however, the number of customers Jan knows personally has shrunk significantly as a percentage of the total customer base for Northcutt Bikes, and many of these new customers are expecting or even demanding very short response times, as that is what attracted them to Northcutt Bikes in the first place. This condition, in addition to the volatility of overall demand, has put a strain on capacity planning. She finds that at times there is a lot of idle time (adding significantly to costs), whereas at other times the demand exceeds capacity and hurts customer response time. The production facility has therefore turned to trying to project demand for certain models, and actually building a finished goods inventory of those models. This has not proven to be too satisfactory, as it has actually hurt costs and some response times. Reasons include the following:

- The finished goods inventory is often not the “right” inventory, meaning shortages for some goods and excessive inventory of others. This condition both hurts responsiveness and increases inventory costs.

- Often, to help maintain responsiveness, inventory is withdrawn from finished goods and reworked, adding to product cost.

- Reworking inventory uses valuable capacity for other customer orders, again resulting in poorer response times and/or increased costs due to expediting. Existing production orders and rework orders are both competing for vital equipment and resources during times of high demand, and scheduling has become a nightmare.

The inventory problem has grown to the point that additional storage space is needed, and that is a cost that Jan would like to avoid if possible.

Another problem that Jan faces is the volatility of demand for bikes. Since she is worried about unproductive idle time and yet does not wish to lay off her workers during times of low demand, she has allowed them to continue to work steadily and build finished goods. This makes the problem of building the “right” finished goods even more important, especially given the tight availability of storage space.

Past Demand

The following shows the monthly demand for one major product line: the standard 26-inch 10-speed street bike. Although it is only one of Jan’s products, it is representative of most of the major product lines currently being produced by Northcutt Bikes. If Jan can find a way to sue this data to more constructively understand her demand, she feels she can probably use the same methodologies to project demand for other major product families. Such knowledge can allow her, she feels, to plan more effectively and continue to be responsive while still controlling costs.

1. Plot the data and describe what you see. What does it mean and how would you use the information from the plot to help you develop a forecast?

2. Use at least two different methodologies to develop as accurate a forecast as possible for the demand. Use each of those methods to project the next four months demand.

3. Which method from question 2 is “better”? How do you know that?

Nitterhouse Masonry Products, LLC, in Chambersburg, Pennsylvania, produces architectural concrete masonry products. The Dover, the largest block in a certain collection, is used primarily for residential retaining walls, and is manufactured to weigh 45 pounds. A quality control inspector for the company randomly selected 17 blocks, and determined that they have an average weight of 46.6 pounds with a sample standard deviation of 3.20 pounds. Assume that the distribution of the weights of the blocks is normal. Please use 4 decimal places for all critical values.

(0.5 pts.) a) Should a z or t distribution be used for statistical procedures regarding the mean? Please explain your answer.

b) Is there any evidence to suggest that the true mean weight is not 45 pounds at a 5% significance level?

Calculate the test statistic

Calculate the p-value.

Write the complete four steps of the hypothesis test below. The work for all parts will be at the end of the question.

c) Calculate the 95% confidence interval for the mean.

d) Explain why parts b) and c) state the same thing. That is, what in part b) is consistent with what in part c)?

e) Is there strong evidence for your decision of "reject the null hypothesis" or "fail to reject the null hypothesis"? Please explain your answer using the results from both the hypothesis test and the confidence interval.

he number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.

​(a) What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate​ chips, inclusive?

​(b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate​ chips?

​(c) What proportion of bags contains more than 1200 chocolate​ chips?

​(d) What is the percentile rank of a bag that contains 1050 chocolate​ chips?

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.

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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.