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

An urn contains 6 white and 10 black balls. The figure gives by
the roll of a dice balance indicates the number of balls that will be drawn without delivery of the ballot box.
Let A be the event defined by:
A: all the balls drawn from the urn are white.
What is the probability that the dice has delivered a 3 knowing that A has realized (Use Bayes' Law)?

how can i apply the concept of normal distribution in civil engineering?

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

Giving a test to a group of students, the grades and gender are summarized below

If one student is chosen at random,

Find the probability that the student was NOT a female that got a "B"

12.19. A study of 300 male and female employees in two manufacturing plants was conducted to explore whether there was gender and age gap in self-esteem. The study’s participants were asked to respond to the statement "I'm happy with myself the way I am" by circling Yes or No. The study found that in in the first plant, 60% of the women and 67% of the men responded Yes. When the same statement was posed to employees in the other plant, 29% of the girls and 48% of the boys responded Yes.

To answer the research questions, two chi square tests were conducted. The first one compared the responses of men and women in the first plant, and the second one compared the responses of men and women in the second plant. The results of the analyses are summarized in the following table. Is there a difference in the responses of men and women? Explain.

Workers in a large plant are expected to complete a particular task in 60 seconds or less. The

production manager believes that the average worker is satisfying that expectation. To

examine the issue she watches eight workers perform the task and measures their times. The

times, which are assumed to be normally distributed, are 58, 53, 63, 62, 57, 55, 53, and 55.

Does this data provide sufficient evidence at the 5% significance level to support the

production manager’s belief?

a. Test statistics:

t

= 2.223

b. P-value= 1.895

c. Do not reject Ho. These data provide insufficient evidence at the 5% level of

significance to support the production manager’s belief.

d. Reject Ho. Yes, these data provide sufficient evidence at the 5% level of significance to

support the production manager’s belief.

The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization's membership is listed below.

1. Find the mean, median, and standard deviation of the number of members per component. (Round your answers to 2 decimal places.)
2. Find the coefficient of skewness, using the software method. (Round your answer to 2 decimal places.)
3. Determine the first and third quartiles. Do not use the method described by Excel. (Round your answers to 2 decimal places.)

4. What are the limits for outliers? (Round your answers to the nearest whole number. Negative amounts should be indicated by a minus sign.)

If you roll two six-sided dice, what is the probability of obtaining the following outcomes?

a)2 or 3

b) 6 and 4

c) At least one 5

d) Two of the same number (two 1s, or two 2s, or two 3s, etc.)

e) An even number on both dice

f) An even number on at least one die

Check the types of sampling methods that should be used in order to draw conclusions about a population at large from what we know about a sample we collected.

Convenience Sample

Voluntary Sample

Random Sample

The below data shows the amount of time (in seconds) that animated Disney movies showed the use of tobacco and alcohol. Test the claim that the mean difference in time of tobacco use vs. alcohol use is equal to zero at the 0.1 significance level. You may want to use a spreadsheet to help you solve this problem

  Tobacco Alcohol

Claim: Select an answer p > 0 u ≠ 0 u ≤ 0 p < 0 u > 0 p ≥ 0 p ≤ 0 p ≠ 0 u < 0 p = 0 u ≥ 0 u = 0

which corresponds to Select an answer H1: u > 0 H0: u ≠ 0 H1: u < 0 H0: u ≤ 0 H1: u ≠ 0 H0: u = 0 H0: p ≥ 0

Opposite: Select an answer u < 0 p > 0 p ≤ 0 u = 0 p ≠ 0 u ≠ 0 u ≥ 0 p ≥ 0 u > 0 p = 0 p < 0 u ≤ 0

which corresponds to Select an answer H1: u < 0 H0: u ≠ 0 H1: u ≠ 0 H0: u ≤ 0 H0: p ≥ 0 H0: u = 0 H1: u > 0

The test is: Select an answer / left-tailed / two-tailed / right-tailed

The test statistic is: Select an answer / -6.969 / -7.119 / -6.289 / -6.729 / -6.609  (to 3 decimals)

The Critical Value is: Select an answer / ± 1.711 / ± 1.47 / ± 1.316 / ± 1.36 / ± 1.867  (to 3 decimals)

Based on this we: Select an answer / Fail to reject the null hypothesis/ Reject the null hypothesis

Conclusion There Select an answer ( does / not does ) appear to be enough evidence to support the claim that the mean difference in time of tobacco use vs. alcohol use is equal to zero.

6. A and B are playing a short game of ping pong where A serves 3 times and B also serves 3 times. If after these six points one of them is ahead the game ends, otherwise they go into a second phase. Suppose that A wins 70% of the points when they serve and 40% of the points when B serves.

Let’s look at the first phase.

a) (3 pts) Find the probability that A or B wins 0, 1, 2, or 3 points when they serve (give the answers separately, so P(A wins 0 points when A serves)= , ...).

b) (4 pts) Find the probability that A scores a total of 4 or more points (so wins in the first phase).

c) (2 pts) Find the probability that A scores 3 points in total (so there is a tie in the first phase).

Now let’s look at cases where the game moves on to the second phase. In this phase there are multiple rounds; in each round each player serves once. They win if they win both points; otherwise it goes to another round. Play continues until someone wins.

d) (4 pts) Find the probability that A wins if it goes to the second phase.

e) (2 pts) Find the probability that A wins (in either the first or second phase).

f) Extra credit (3 pts): find the expected number of points played.

The retail stores in the North Towne Square shopping center are the following:

00 Elder-Beerman 08 Kay-Bee Toy & Hobby 16 Pearle Vision Express
01 Sears 09 Lion Store 17 Dollar Tree
02 Deb Shop 10 Bootleggers 18 County Seat
03 Frederick's of Hollywood 11 Formal Man 19 Kid Mart
04 Petries 12 Leather Ltd. 20 Lerner
05 Easy Dreams 13 B Dalton Bookseller 21 Coach House Gifts
06 Summit Stationers 14 Pat's Hallmark 22 Spencer Gifts
07 E. Brown B. Opticians 15 Things Remembered 23 CPI Photo Finish
24 Regis Hairstylists

to. If you select the random numbers 11, 65, 86, 62, 06, 10, 12, 77 and 04, what stores do you need to contact to conduct a survey? Forman Man, Summit Stationers, Bootleggers, Leather Ltd, Petries.
b. You must apply the systematic sampling procedure. A sample of size five (n = 5) is necessary and the first randomly selected sample element is Frederick's of Hollywood. Which stores make up your sample?

Did you come across any notable data analysis tools during your research for the activity submission? Share with your fellow classmates any interesting or useful hardware or software tools that you have come across. Discuss your thoughts on the applicability of this tool in your context or field of interest, as well as any ways in which you think this tool could be beneficial to a specific industry or job role.