The Federal Drug Administration wishes to determine whether the claims that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self- reported colds is recorded after three years. Number of colds in 3 years: Vitamin C group: 3, 8, 6, 7, 4, 9, 2, 5, 7, 11, 10, 8, 7, 6, 7 Placebo group: 8, 8, 7, 10, 11, 4, 3, 7, 6, 8, 4, 10, 6, 8,5 The value of the numerator (either + or -) in the t test formula for Problem 3 is _____. Then what is the degrees of freedom and what is the derived t value ? Also, what can be concluded from the statistical analysis and what significance level should be reported?

(I want to compare my answers to yours, because I have different answers than what was given to me earlier on this site, and I don;t understand why...thank you.)

In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?

A box contains 4 white, 3 red, and 3 black marbles. One marble is chosen at random, and it is not black. Find the probability that it is white. (Enter your answer as a fraction.)

Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.3. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)

Companies X, Y and Z all manufacture a specific component required to make a touch screen tablet. Of these three companies, X shipped 1024 components, Y shipped 512 and Z shipped 256. The percentage of defective components produces by each company is 4%, 5% and 14% for X, Y and Z, respectively. What is the probability that a given defective component came from Company Y?

Please enter your answer as a decimal with 3 significant digits, e.g., .250 or 0.250.

Discuss the advantages and disadvantages of using R to analyze data compared to a spreadsheet tool such as Microsoft Excel or Tableau. Provide specific examples to illustrate your ideas.

1. What is the median of the sample of size​ 30?

2.For each data set recalculate the mean and​ median, assuming that the individual whose IQ is 108, and108 is accidently recorded as 180. What is the median of the new sample of size​ 30?

1. A grocery store counts the number of customers who arrive during an hour. The average over a year is 29 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals. Find the probability that at least two customers arrive in a particular 2 minute period.

2. Label each as one of the following

Exponential

Poisson

Binomial

Uniform

1. a constant probability density and charts as a rectangle
2. fixed number of trials with only 2 possible outcomes and the trials are independent  
3. models the time until some specifi event occurs such as equipment failure  
4. events happen with a known average rate and independently of the time since the last event  

An email system sends incoming mail to either the In-Folder (I) or the Trash Folder (T). You classify incoming mail as Useful (U), in which case you want it sent to I, or as a Nuisance (N) in which case you would like it sent to T. If incoming mail is U, the system sends it to T with probability 0.1. If the incoming mail is N, the system sends it to I with probability 0.05. Suppose a proportion 0.35 of your incoming mail is N.

What is the probability that an incoming mail is sent to T?

What is the probability that an incoming mail is U given that it is sent to T?

One of the quirks of the ground is occasional acid fog. Only 150 grounders are immune to acid fog out of a total of 3000 grounders. For a random group of 250 grounders in an acid fog;

A. (6 points) What is the expected value and standard deviation of the number of survivors? (HINT: It might be useful to think about the Binomial distribution here.) (Your answer here)

B. (8 points) what is the approximate probability that the number of survivors is at least 20? (Your answer here)

C. (6 points) Verify the conditions needed to compute the probability in Part (B) above. (Your answer here)

QUESTION 4

1. You gather data from 28 parolees who are currently enrolled in job training programs while on parole. You find that over the past year, they have been cited an average of 3.2 times for technical parole violations with a standard deviation of 1.2.

   Using this information, construct a 99% confidence interval for the overall mean technical violation rate for parolees who are enrolled in job training programs. Round all answers to 2 decimal points (0.00). Be sure to interpret your results.

he weight of an organ in adult males has a​ bell-shaped distribution with a mean of 320 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following. ​

(a) About 99.7​% of organs will be between what​ weights?

​(b) What percentage of organs weighs between 230 grams and 410 ​grams? ​

(c) What percentage of organs weighs less than 230 grams or more than 410 ​grams? ​

(d) What percentage of organs weighs between 275 grams and 455 ​grams?

Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players: x₁; n₁ = 21

Weights (in lb) of pro basketball players: x₂; n₂ = 19

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to one decimal place.)

(c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players?

Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players.Because the interval contains both positive and negative numbers, we cannot say that professional football players have a higher mean weight than professional basketball players.    Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players.

(d) Which distribution did you use? Why?

The standard normal distribution was used because σ₁ and σ₂ are unknown.

The standard normal distribution was used because σ₁ and σ₂ are known.    

The Student's t-distribution was used because σ₁ and σ₂ are unknown.

The Student's t-distribution was used because σ₁ and σ₂ are known.

What is the probability that if Paul, Mary, and Susan are in a group of 7 people randomly seated in 7 chairs, they want to be in consecutive chairs. What is the probability if the chairs are set in a circle?

A soccer ball manufacturer wants to estimate the mean circumference of​ mini-soccer balls within 0.05 inch. Assume the population of circumferences is normally distributed.

​(a) Determine the minimum sample size required to construct a 95​% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.

​(b) Repeat part​ (a) using a population standard deviation of 0.35 inch.

​(c) Which standard deviation requires a larger sample​ size? Explain

•Vocabulary list (define)

normal distribution

Gaussian distribution

Standard normal

Z score (or Z value)

•What is the area under a normal distribution?

•What is the area under any distribution?

Find the standard deviation for a set of data that has a mean of 100 and 95% of the data falls between 70 and 130.

** Please show me the procedure, thanks!!!