2,000 men were enrolled in a study. They were followed by investigators for 4 years. Each year, the men were tested for prostate cancer. After yr 1 , there were no cases, but 20 men were lost to follow up. After 2nd year, there were 10 cases of cancer and 25 men were lost to follow up. At the end of the 3rd year, there were 16 cases and 3 men were lost. At the end of the 4th year, there were 25 cases &30 men lost to follow up. What is person-time incidence rate of cancer in this group?

1. John Connor and his friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of death and dismemberment for each activity under the various possibilities for sentient cybernetic organisms they may encounter. They have no idea which of the terminators, the T-X, the T-1000, or the T-100, they might encounter on their outing.

1. If the group is optimistic, what decision should they make? [5 Marks]
2. If the group is conservative, what decision will they make? [5 Marks]
3. If the group chooses to minimize their maximum regret, what activity will they choose? [5 Marks]
4. If the probabilities of the T-X, T-1000, and T-100 are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion? [5 Marks]

Three instructors in a coordinated course, T1, T2, and T3 evaluates axam papers. T1 evaluates 20% of the exam papers, T2 pevaluates 30% and T3 evaluates 50%. The three theachers make the following proportions of errors (E) while evaluating the exam papers: 0.008, 0.008, and 0.003 respectively. If a randomly selected exam paper has an error (E), what is the probability it is from instructor T1?

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 5.9% with a standard deviation of 7.1​%.

If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first.

Suppose that a long distance taxi service owns 4 vehicles. These are of different ages and have different repair records. The probabilities that, on a given day, each vehicle will be available for use are: 0.90, 0.90, 0.80, 0.70. Whether one vehicle is available is independent of whether any other vehicle is available. a. Find the probability distribution for the number of vehicles available for use on a given day. b. Find the expected number of vehicles available for use on a given day. c. Find the standard deviation of the number of vehicles available for use on a given day. Round your answer to four decimal points

Q12: The following data are from a study of the relationship between average consumption of saturated fat (in grams) and cholesterol level (in milligram per hundred milliliters) of eight males:

Below are some of the summaries of this data:

∑?=413, ∑?=1514, ????=1277.875, ????=5591.5 and ????=2536.75

(a) Compute the estimates of regression coefficients β0 and β1 and write the fitted regression line.

(b) Does the amount of fat consumption determine the cholesterol level? Carry out a hypothesis test to support your answer at 2% significance level.

(c) Construct a 98% confidence interval for β1.

(d) Calculate the variability in the cholesterol level not explained by the amount of fat consumption and interpret it.

Lindsay is 30 years old and has a new job in web development. She wants to make sure that she is financially sound by the age of 55, so she plans to invest the same amount into a retirement account at the end of every year for the next 25 years. (a) Construct a data table in Excel that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $10,000 at return of 6%, what would be the balance at the end of the 25th year? Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Round your answer to a whole dollar amount. $ (b) Develop a two-way table for annual investment amounts of $5,000 to $20,000 in increments of $1,000 and for returns of 0% to 12% in increments of 1%. From the 2-way table, what are the minimum annual investments Lindsay’s must contribute for annual rates ranging from 6% to 11%, if she wants to accrue a final payout of at least $1 million? Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Annual Return Minimum Annual Investment 6% $ 7% $ 8% $ 9% $ 10% $ 11% $

***Please use excel and upload excel screenshot with formula

Use the standard normal table to find the​ z-score that corresponds to the given percentile. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score. P75

A computer consulting firm presently has bids out on three projects. Let

A_i = {awarded project i},

for

i = 1, 2, 3,

and suppose that

P(A₁) = 0.22,

P(A₂) = 0.25,

P(A₃) = 0.28,

P(A₁ ∩ A₂) = 0.13,

P(A₁ ∩ A₃) = 0.03,

P(A₂ ∩ A₃) = 0.06,

P(A₁ ∩ A₂ ∩ A₃) = 0.01.

Express in words each of the following events, and compute the probability of each event.

(a)

A₁ ∪ A₂

Express in words the event.

awarded only 1 awarded only 2    awarded neither 1 nor 2 awarded either 1 or 2 awarded either 1 or 2 (or both)

Compute the probability of this event.

(b)

A₁' ∩ A₂'

[Hint:

(A₁ ∪ A₂)' = A₁' ∩ A₂']

Express in words the event.

awarded only 1 awarded only 2    awarded neither 1 nor 2 awarded either 1 or 2 awarded either 1 or 2 (or both)

Compute the probability of this event.

(c)

A₁ ∪ A₂ ∪ A₃

Express in words the event.

awarded 1 but neither 2 or 3 awarded 3 but neither 1 nor 2    awarded at least one of these three projects awarded all of the three projects awarded none of the three projects

Compute the probability of this event.

(d)

A₁' ∩ A₂' ∩ A₃'

Express in words the event.

awarded 1 but neither 2 or 3 awarded 3 but neither 1 nor 2    awarded at least one of these three projects awarded all of the three projects awarded none of the three projects

Compute the probability of this event.

(e)

A₁' ∩ A₂' ∩ A₃

Express in words the event.

awarded 1 but neither 2 or 3 awarded 3 but neither 1 nor 2    awarded at least one of these three projects awarded all of the three projects awarded none of the three projects

Compute the probability of this event.

(f)

(A₁' ∩ A₂') ∪ A₃

Express in words the event.

awarded only 1 or 2 awarded only 3    awarded neither of 1 and 2, or awarded 3 awarded either of 1 or 2, but not awarded 3 awarded at least one of these three projects

Compute the probability of this event.

In a certain​ distribution, the mean is

40

with a standard deviation of

5

At least what fraction of the numbers are between the following pair of​ numbers?

30

and 50

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 3inches.

(a) What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of eleven 18-year-old men is selected, what is the probability that the mean height x is between 67 and 69 inches? (Round your answer to four decimal places.)

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.3 years, and standard deviation of 1.7 years. If 16 items are picked at random, 2% of the time their mean life will be less than how many years? Give your answer to one decimal place.

A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 10% margin of error at a 98% confidence level, what size of sample is needed?
The political candidate will need to sample___ people.

A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 10% margin of error at a 98% confidence level, what size of sample is needed?
The political candidate will need to sample___ people.

You measure 38 textbooks' weights, and find they have a mean weight of 32 ounces. Assume the population standard deviation is 7.4 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
I am 90% confident that the mean weight of textbooks is between___ and___ ounces.

A researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 30 bacteria reveals a sample mean of ¯x=76x¯=76 hours with a standard deviation of s=6.8s=6.8 hours. He would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 99% level of confidence.
What sample size should you gather to achieve a 0.5 hour margin of error?
He would need to sample___ bacteria.

There are 4 people in a room. What’s the probability that there are two people born on the same day of the week? (Assume all birthdays are independent and are uniformly distributed over the seven days of the week.)

You want to know if Apple and Android phone users use different mobile apps for social networking. You collect the following data.

The null hypothesis for this chi-square test would be?

How many degrees of freedom are there for this chi-square test?

What is the expected value of Apple Snapchat users?

What is the expected value of Android Instagram users?

Calculate the chi-square. Which is the appropriate description of the result?

Group of answer choices

1. The result is significant. This suggests that the two variables are not independent.

2. The result is significant. This suggests that the two variables are independent.

3. The result is non-significant. This suggests that the two variables are independent.

4. This result is non-significant. This suggests that the two variables are not independent.

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y ˆ = b 0 + b 1 x y^=b0+b1x , for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0.5 0.5 1.5 1.5 2 2 2.5 2.5 3.5 3.5 4 4 5.5 5.5 Overall Grades 96 96 94 94 90 90 86 86 85 85 80 80 70 70 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places. According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y ˆ y^ is given by? Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. Determine the value of the dependent variable y ˆ y^ at x=0 x=0 . Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.