Statistics:

Construct a stem and leaf diagram, a frequency distribution table, plus develop a bar chart, pie chart, histogram, polygon and an ogive from the following data set.

When you construct the pie charts, bar graphs, etc. Use the calculation of 2^K to find the number of classes you will need to construct the frequency distribution table. You will need to use lower class limits, lower-class boundaries, midpoints upper-class boundaries, upper-class limits, frequency, relative frequency, and cumulative frequency.

DATA:

90, 92, 94, 100, 100, 91, 95, 96, 93, 23, 31, 57, 42, 59, 48, 58, 49, 37, 62, 75, 83, 88, 89, 70, 71, 79, 85, 77, 69, 82, 85.

The Pew Research Center took a random sample of 2928 adults in the United States in September 2008. In this sample, 53% of 2928 people believed that reducing the spread of acquired immune sample deficiency disease (AIDS) and other infectious diseases was an important policy goal for the U.S. government.

1. If the significance level α=0.05, should we reject or fail to reject the null hypothesis? How would you interpret your results of hypothesis testing?        REJECT H_O      DO NOT REJECT H_O

INTERPRET:

2. Based on the above questions, what is the difference between confidence interval and hypothesis testing? When should we use confidence interval and when should we use hypothesis testing?

Directions: Answer the following questions. Round probabilities to four digits after the decimal. For full credit, you will need to show your work justifying how you determined numerical values. You may consider adding additional blank space to this document, printing, filling out by hand, and then uploading a scan or pictures of your answers. You may also re-write these questions on a separate sheet of paper and use as much space as you need to answer the questions.

Charles is a notoriously bad student who never studies for his quizzes. One day, his teacher gives a four question, multiple-choice quiz. Each question has five answer options (a, b, c, d, and e) and each question has only one correct answer option. Since Charles doesn’t study, we might assume that he is going to guess on each of the four questions.

Let X be a discrete random variable representing the number of questions Charles may correctly answer.

Part 1. (5 points) Complete the following probability distribution table:

Part 2. (4 points) Using the table you constructed, find the expected value, μ, and the standard deviation, σ. Please show your work.

Part 3. (2 points) A statistician might consider an outcome with probability less than 0.05 to be “unusual”. Based on this criterion, should we be surprised if Charles guesses three or more questions correctly? Please explain briefly.

Part 4. (2 points) Alternatively, a statistician might consider an outcome to be “unusual” if it is more than two standard deviations away from the mean. Based on this criterion, should we be surprised if Charles guesses three or more questions correctly? Please explain briefly.

Part  5. (2 points) Suppose Charles happens to get three out of four questions correct. When computing the probabilities in problem 1, we assumed that Charles was guessing on every question; based on your answers to problems 3 and 4, do you think our assumption is plausible? What is an alternative explanation for Charles’s performance?

The following eight observations were drawn from a normal population whose variance is 100:

12

8

22

15

30

6

29

58

Part A

What is the standard error of the sample mean, based on the known population variance? Give your answer to two decimal places in the form x.xx

Standard error:

Part B

Find the lower and upper limits of a 90% confidence interval for the population mean. Give your answer to two decimal places in the form xx.xx

Lower limit:

Upper limit:

Part C

True or false:

If the population was not normally distributed the confidence interval calculation above would not be valid. Answer by writing T or F in the space provided.

Answer:

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X = $50.50 and S = 20. Assuming that the amount spent follows a normal distribution, construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. assuming that the amount spent follows a normal distribution.

A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a “bar” as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. To convert the data into useful information, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report, determine the critical value, and sampling error. Explain what management can learn from the 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report.

#9.

Assume that human body temperatures are normally distributed with a mean of 98.23 °F and a standard deviation of 0.63 °F.

1. A hospital uses 100.6 °F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a​ fever? Does this percentage suggest that a cutoff of 100.6 °F is​ appropriate?

2. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature​ be, if we want only​ 5.0% of healthy people to exceed​ it? (Such a result is a false​ positive, meaning that the test result is​ positive, but the subject is not really​ sick.)

a. The percentage of normal and healthy persons considered to have a fever is __

a1. Does this percentage suggest that a cutoff of 100.6 °F is​ appropriate?

b. The minimum temperature for requiring further medical tests should be __ if we want only​ 5.0% of healthy people to exceed it.

#8

A survey found that​ women's heights are normally distributed with mean 63.4 in and standard deviation 2.4 in. A branch of the military requires​ women's heights to be between 58 in and 80 in.

a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too​ tall?

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest​ 1% and the tallest​ 2%, what are the new height​ requirements?

An automobile license plate consists of 3 letters followed by 4 digits. How many different plates can be made:

a. If repetitions are allowed?

b. If repetitions are not allowed in the letters but are allowed in the digits?

c. If repetitions are allowed in the letters but not in the digits?

Suppose you choose a coin at random from an urn with 3 coins, where coin i has P(H) = i/4. What is the pmf for your prior distribution of the probability of heads for the chosen coin? What is your posterior given 1 head in 1 flip? 2 heads in 2 flips? 10 heads in 10 flips?Hint: Compute the odds for each coin first.

1. Describe how the education of healthcare professionals impacts the delivery of healthcare services in the community and around the world.

2. Describe two capabilities/competencies required of today’s healthcare professionals in addition to those related to their professional specialization and how these additional capabilities/competencies assist in the long-term process of optimizing global health.

We are given 3 urns as follows: Urn A contains 3 red and 5 white marbles, Urn B contains 2 red and one white marble, Urn C contains 2 red and 3 white marbles. Construct the probability tree. Suppose that a urn is randomly selected and a marble is drawn from the selected urn. If the marble is red what is the probability that it came from urn A?

Using the weather Markov chain simulate the weather over 10 days by flipping a coin to determine the chances of sunny or cloudy weather the next day according to the Markov chain's transition probabilities. If currently sunny, flip once and a head means sunny the next day and a tail means cloudy the next day. If currently cloudy flip twice and when either flip is a head it is sunny the next day and when both flips are tails it is cloudy the next day. To start, assume that the previous day was sunny. what fraction of the 10 days was sunny?

Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: H 0 : p M = p F H 1 : p M ≠ p F H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : μ M = μ F H 1 : μ M ≠ μ F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F The test is: left-tailed right-tailed two-tailed Based on a sample of 40 men, 45% owned cats Based on a sample of 40 women, 50% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

In a class of 87 people, 27 wear glasses, 32 are blonde, and 38 are neither blonde nor wear glasses. Find the probability that a student chosen at random will have blonde hair and wear glasses?