An exam has 8 multiple choice questions. Each question has 4 possible answers, only one of which is correct. If a student takes this exam and answers all questions at random, what is the probability that the student answers

(a) only the first and the last question correctly?

(b) only 2 questions correctly?

(c) at least 2 questions correctly?

Suppose that an investigation of the association between regular physical activity and ovarian cancer revealed that the incidence rate of ovarian cancer among women who engaged in regular physical activity was 30 per 100,000 women-years of follow-up, whereas the rate among women who did not engage in regular activity was 45 per 100,000 women-years of follow-up.

A. use these data to compute the incidence rate ratio of ovarian cancer for women who are physically active versus women who are not.

B. State in woads you interpretation of this measure.

C. Computer the incidence rate difference of ovarian cancer for women who are physically active versus women who are not.

D. State in words your interpretation of this measure.

E. If there were not association between regular physical activity and ovarian cancer, what would be the numeric values of the incidence rate ratio and incidence rate difference.

A computer chip manufacturer finds that, historically, for ever 100 chips produced, 85 meet specifications, 10 need reworking, and 5 need to be discarded. Ten chips are chosen for inspection. A) What is the probability that all 10 meet specs? B) What is the probability that 2 or more need to be discarded? C) What is the probability that 8 meet specs,1 needs reworking, and 1 will be discarded?

In testing the difference between the means of two normally distributed populations, if μ₁ = μ₂ = 50, n₁ = 9, and n₂ = 13, the degrees of freedom for the t statistic equals ___________.

19,20,21,22

When comparing two independent population means by using samples selected from two independent, normally distributed populations with equal variances, the correct test statistic to use is ______.

z,F,t, t^2

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units, the correct test statistic to use is _________.

z, None of the other choices is correct, t, F, chi-square

In testing the difference between the means of two normally distributed populations using independent random samples, the correct test statistic to use is the

F statistic, chi-square statistic, None of the other choices is correct, t statistic, z statistic.

In general, the shape of the F distribution is _________.

skewed right, skewed left, binomial, normal

The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.4 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?


b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.



c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?



d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.

What z-score separates the highest 3 percent of the standard normal distribution from the lower 97 percent (i.e. represents the 97th percentile)?

Assume that you are planning to have a party at your house. You really would like to have the party outside in the sun, but there is a chance that it might rain. You have two decisions to make – whether or not you will watch the forecast and then whether to have the party inside or outside. If you choose to watch the forecast, it will either tell you that the weather will be sunny or that it will be rainy. If you choose to watch the forecast, you will not have to make the location decision until after you see the forecast. If you do not watch the forecast, you do not get to know what the forecast would have said had you watched it – you need to make the location decision without the knowledge of the forecast. However, the forecast is imperfect (probabilities are below). It also costs you some time, and you are already cutting it close in terms of getting ready.

Your task is to draw the decision tree for this situation, answer some questions about the decision tree, and recommend a course of action on the basis if your analysis.

The information you will need:

Probabilities (note that p(A|B) signifies the probability of event A given that event B has occurred – it is a conditional probability).

p(forecast says it will be sunny) = 0.95

p(it is sunny|forecast said it would be sunny) = 0.99

p(it is sunny|forecast said it would be rainy) = 0.15

p(sunny) = 0.948 [hint: this is to use on the branch of the tree where you decide not to watch the forecast]

Utilities (note that U(case X) represents the utility of case X)

U(watch forecast, party indoors, sunny weather) = 0.3

U(watch forecast, party indoors, rainy weather) = 0.4

U(watch forecast, outdoors, sunny weather) = 0.9

U(watch forecast, outdoors, rainy weather) = 0.0

U(do not watch forecast, indoors, sunny weather) = 0.4

U(do not watch forecast, indoors, rainy weather) = 0.5

U(do not watch forecast, outdoors, sunny weather) = 1.0

U(do not watch forecast, outdoors, rainy weather) = 0.1

(a) (10 points): Draw the decision tree for this problem. Include clear labels for all branches. Include all probabilities and utilities.

(b) (10 points): If you choose to watch the forecast and it says that the weather will be sunny, should you have the party indoors or outdoors? What is your expected utility for this choice?

(c) (5 points): What should your sequence of decisions be? In other words, should you watch the forecast? If you do watch the forecast, what is the optimal location decision for each of the two possible forecast reports? What is your expected utility for the overall decision situation?

d) (10 points): Analyzing a simple party problem might seem silly. However, the structure of this tree has many important applications in engineering. Think of a project management situation that could be described by this structure of decision tree. Write a one-paragraph description of the decision situation you think of (like the description at the beginning of this question), and re-draw the tree with new labels on the branches. You do not need to include any probabilities or utilities on your new tree.

Assume that the number of new visitors to a website in one hour is distributed as a Poisson variable with λ = 4.0. What is the probability in any given hour that two or more new visitors will arrive at the website?

Round to four decimals and use leading zeros if necessary.

Explain how a sample, a sampling distribution, and a population differ. What are the means and standard deviation for each of these?

Suppose a friend of yours is hosting a wine tasting. His wine supply includes three different types of deluxe wine. All bottles come from the same winery and all wines were harvested in 2017. He currently owns 8 bottles of zinfandel, 10 bottles of merlot, and 12 bottles of cabernet. Throughout the wine tasting, your friend will only open a new bottle of wine when there are no other bottles of wine open at the time.

a. State any and all event definitions.

b. Suppose the wine tasting will consist of two bottles chosen at random. How many different sequences of offerings are there?

c. Create a tree diagram of the sample space and label all events and their corresponding probabilities.

d. What is the probability that all bottles in the wine tasting are of the same type of wine?

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting this disease. A family has three children. The probability of this family having at least one child who inherited this genetic disease is:

In a population survey of patients in a rehabilitation hospital, the mean length of stay in the hospital was 12.0 weeks with a standard deviation equal to 1.0 week. The distribution was normally distributed. What is the percentile rank for each of the following z scores? Enter the percentile rank to the right of each z score. Assume a normal distribution.

a) 1.23 _____

b) 0.89 ______

c) -0.46 _____

d) -1.00 ______

1. Your team would like to calculate the attributable risk or attributable proportion of CHF death rates due to smoking 1-14 and 15-24 cigarettes per day separately for males and females. Do you notice any differences within and between these groups in death rates due to CHF based on the different number of cigarettes smoked per day?
2. What can the team conclude about the death rate due to CHF for males and females separately when zero cigarettes per day are smoked? How do they compare?

   Your quality improvement Team is revisiting the following patient readmissions and would like to predict the number of readmissions based on the number of drugs administered.

A real estate agent (Sue Bays Realty) wants tot study the relationship between the size of a house and its selling price. The table below presents the size in square feet and the selling price in thousands of dollars, for a sample of houses in a suburban neighborhood.

Calculate the correlation between these two variables.

Calculate the Predicted Value for each size/price value.

If a linear regression model were fit, what would the value of the slope and the value of the y-intercept be?

1. Your team needs to decide how to measure the effectiveness of this measure. You think the best way would be to compute the values of the sensitivity, specificity and predictive value. Show your work and provide an interpretation of these measures.
2. On the basis of your results, is this an effective measure? Why or why not?
3. Once you assess the effectiveness of this measure, and your team feels confident that this is an appropriate measure to use, the Health Administrator of the Unit asks your team to examine the odds of patients being readmitted for those who were administered at least 3 drugs. Calculate the odds ratio and explain this finding to your administrator.