Biostatistics with R

- Solve the following by evaluating the test statistic and p value. Suppose that the population mean of systolic blood pressure in the US is 115. We hypothesize mean systolic blood pressure is lower than 115 among people who consume a small amount (e.g., around 3.5 ounces) of dark chocolate every day. Assume that systolic blood pressure, X, in this population has a Normal distribution. To evaluate our hypothesis, we randomly selected 100 people, who include a small amount of dark chocolate in their daily diet, and measured their blood pressure. If the sample mean is x¯ = 111 and the sample variance is s = 32, can we reject the null hypothesis at 0.1 confidence level?

- Solve the following using the Confidence Interval Hypothesis Test approah and t.test() Approach. Use the Pima.tr data set to evaluate the hypothesis that the population mean of diastolic blood pressure for Pima Indian women is not 70.

library(MASS)

data("Pima.tr")

#str(Pima.tr)

?Pima.tr

I've noticed that there's this misconception that folks who disagree with our general classroom-perspective are considered uneducated. This includes Dennis (who rejected life-saving measures due to religious reasons) or animal rights stakeholders (like the trauma surgeon).

There's a lot of science that shows us that facts (read: education) don't help to change people's minds

Now consider the following questions for this discussion:

When talking with someone you know really well, what kind of things do you get out of that interaction? Think along the lines of empathy, understanding, companionship, feeling listened to.

How does your communication style change when trying to change someone's mind? What do you get out of being "right"? Do you think the person gets something out of being "wrong"?

What's it like to be on the other side of the conversation when someone is trying to convince you of something?

How might we try to communicate more effectively around these controversial subjects?

who are examples of under appreciated stakeholders in the automotive company TESLA that generally are forgotten min 3?

Prof. Washington has a self-managed retirement plan through his University and would like to retire in 10 years and wonders if his current and future planned savings will provide adequate future retirement income. Here’s his information and goals.

▪ Prof. Washington wants a 25-year retirement annuity that begins 10 years from today with an equal annual payment equal to $70,000 today inflated at 3% annually over 10 years. His first retirement annuity payment would occur 10 years from today. He realizes his purchasing power will decrease over time during retirement due to the inflation.

Prof. Washington currently has $280,000 in his University retirement account. He expects these savings and any future deposits into his University and any other retirement account will earn 7.5% compounded annually. Also, he expects to earn this same 7.5% annual return after he retires. Answer the following questions to help Prof. Washington finalize his retirement planning.

1. What is Prof. Business’ desired annual retirement income in the first year, i.e., the retirement income he wants 10 years from today?

2. Assuming that inflation is zero from year 10, how much will Prof. Washington need 10 years from today to fund his desired retirement annuity?

3. Assume that inflation is zero from year 10. In addition to the $280,000 balance today, Prof. Washington will fund his future retirement goal from question 2 by making 10 annual equal deposits at 7.5% compounded annually into his retirement accounts starting a year from today (the last deposit will be made when Prof. Washington retires). How large does this annual deposit need to be in addition to the initial $280,000 invested in Prof. Business’ retirement fund?

4. Assume that inflation is 3% during the entire period, even after retirement. Prof. Washington is worried about his purchasing power eroding during retirement. He would like his first retirement withdrawal to be equal to the amount you found in #1, and then he increase each successive retirement withdrawal by 3% annually over the remaining 24 withdrawals. How much will Prof. Washington need now at retirement given Prof. Washington's 7.5% expected return?

5. In addition to the $280,000 balance today, Prof. Washington will fund his adjusted future retirement goal from question 4 by making 10 annual equal deposits at 7.5% compounded annually into his retirement accounts starting a year from today (the last deposit will be made when Prof. Washington retires). How large does this annual deposit need to be in addition to the initial $280,000 invested in Prof. Washington’s retirement fund?

1. As consumers compare prices across firms in a market more(as they engage in more search), what happens to the elasticity of demand for the individual firms in the market? What happens to the prices that the firms charge? Does the quantity provided in the market move closer to or further away from the efficient quantity? Please explain.

The estimated regression equation for predicting the number of speeding tickets from a driver’s age is given as Y = 5 – 0.06X. For every year older an individual gets, the estimated number of speeding tickets

Need to know which is the answer:

Increases by 5 tickets

Decreases by 5 tickets

Decreases by 0.06 tickets

Does the pursuit of maximum profit by individual business owners benefit only themselves or does their self interest sometimes and somehow also benefit the broader society? Include in your discussion how each of the characteristics of a competitive market is relevant to achieving a social benefit from private profit seeking behavior.

Suppose you are a polluter with very high marginal abatement costs. Rank the following policies from the one that is most favourable for you to least favourable: uniform standard, individual standard, emission tax, marketable permits distributed initially without charge. Explain the reasons for your ranking and illustrate graphically

2) Male company employees aged 21 to 26 are found to drive an average of 19484 km a year. The annual mileage is normally distributed with a standard deviation of 6812 km. The company has decided to levy a user fee on those employees who are in the top 30%. Find the yearly mileage total of those who will be charged a user fee.

3) If α = 0.06, standard deviation is s = 3.15, sample mean is x= 12.7, and n = 500, find the confidence interval for the population mean.

On I-5, you see the bright pink Almond Roca sign. You know they produce Almond Roca, but you wonder if they have ever thought about Brazil Roca, or Cashew Roca! You think these would be delicious, and you aren’t really an almond fan.

Industry Background

Candy has been a part of our world for thousands of years. The first candy was made from honey. It was reserved, as were most good things, for the wealthy for a long time. In the Industrial Revolution, candy started to be more widely available. Latest figures place candy sales at $118 billion world-wide.

There are about 100 different candy manufacturers in the US, both large and small, from Mars, Inc. which is the 6^th largest company in the US with $33 billion in sales; to local Almond Roca, with an estimated $50 million in sales.

Current Issues

One of the biggest issues facing this company is the rise in prices of raw materials, especially the iconic almond, which due to drought in California, has seen a price rise in recent years (although market forces are starting to correct for this).

In order to diversify their product, Almond Roca, Inc., has started to expand its repertoire to including other nuts, such as cashews and macadamia nuts. They are considering expanding to even more types of nuts, even mixed nuts!

Part 1 – Manufacturing Methods

Almond Roca is considering three nut mixes for inclusion in a new product line, Mixey Nuts!: Regular Mix, Deluxe Mix, and Holiday Mix. Each mix is made from 5 nuts, in different combinations.

The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut.

The Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.

An accountant at Almond Roca, Inc., analyzed the cost of packaging materials, sales price per pound, etc, and determined that the profit contribution per pound is $1.65 for the Regular Mix, $2.00 for the Deluxe Mix, and $2.25 for the Holiday Mix. The price of the nuts can vary from month to month.

The estimate the customer orders for the different types to be as follows:

The president of Almond Roca wants to commit to these a minimum, even if not immediately profitable, in order to introduce these new mixes to the market.

Report:

Summarize this problem, and discuss the following topics, in a Word Document:

1.     The cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes.

2.     The optimal product mix and the total profit contribution.

3.     Recommendation regarding how the total profit contribution can be increased if additional quantities of nuts could be found.

4.      A recommendation as to whether Almond Roca should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought.

5.      Recommendations on how profit contribution could be increased (if at all) if Almond Roca does not satisfy the minimums listed above.