Twelve sheep were fed a special diet consisting of dried grass and barley for three months. At the end of the period the plasma insulin concentration (??/??) was determined for each sheep. The data are: 20.5 26.2 18.8 21.2 22.1 21.2 25.4 26.8 22.9 22.8 30.8 28.4

a) Find the mean, median and mode.

b)Find the first and third quartiles.

c) Find the range, variance and standard deviation.

d) Find the 40th percentile ?40.

e) Find the percentile rank of 25.4.

f) Find the interquartile range (???). What does the ??? explain about the distribution of the plasma insulin concentration of the twelve sheep?

g) Identify the outliers if there are any?

h) Construct the box-plot for the data set and comment on the shape of the distribution of the data.

67% of adults age 55 or older want to reach their 100th birthday. You randomly select 8 adults age 55 years or older and ask them if they want to reach their 100th birthday. The random variable represents the number of adults ages 55 or older who want to reach their 100th birthday.

a) What is the probability that exactly 5 of them say they want to reach their 100th birthday?

b) What is the probability that at most 5 of them say they want to reach their 100th birthday?

c) What is the probability that more than 4 adults say they want to reach their 100th birthday?

d) What is the probability that at least 5 of them say they want to reach their 100th birthday?

e) What is the probability that less than 4 adults say that they want to reach their 100th birthday?

f) What is the mean and standard deviation of the binomial variable?

Please show your work!

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51.1 and 51.5 min. Round the answer to 3 decimal places. P(51.1 < X < 51.5) =

For a standard normal distribution, find: P(z > 2.04)

For a standard normal distribution, find: P(-1.04 < z < 2.04)

For a standard normal distribution, find: P(z > c) = 0.6332 Find c.

Problem#5: The Birthday Problem (10pts) In your classroom there are 45 students, assume that none of them is born on February 29, and hence consider only common years (365 days) [do not consider leap years]. 1- Take a student randomly from the class, what is the probability that he have the same birthday as yours? 2- What is the probability that there is at least one student in the class having the same birthday as yours? 3-What is the probability that there is no repeated birthday date in the class (all the 45 birthdays being different)? Comment on the value you found 4- The instructor decides to nominate 5 students randomly to deliver a presentation next class, • How many groups (of five students) are possible? • What is the probability that you are among the selected students?

What is the difference between weighted mean and regular mean in math?

A researcher plans to do an experiment in the college setting concerning the effects of class size on attendance in a first year law course. He has four levels of size, namely, 15, 25, 40, and 60 students. Four colleges are involved in the study, each having eight first-year law classes, two of each class size. The researcher can assign students at random to a class within a college. All professors teach four classes; the dependent variable is grades measured after one semester. Discuss the problems of control in this situation. Consider possible uncontrolled variables and variables that are or might be controlled. Is there a possibility of confounding variables in this research situation? State one or more hypotheses for this experiment.

AM -vs- PM Test Scores: In my AM section of statistics there are 22 students. The scores of Test 1 are given in the table below. The results are ordered lowest to highest to aid in answering the following questions.

(a) The value of P₉₀ ---->

(b) Complete the 5-number summary.

SAS code please.

Two cholesterol-lowing medications (statins) and a placebo were given to each of 10 volunteers with total cholesterol; readings of 240 or higher. After 6 weeks, the flowing total cholesterol values were recorded:

Stain A: 220 190 180 185 210 170 178 200 177 189

Stain B: 160 168 178 200 172 155 159 167 185 199

Placebo: 240 220 246 244 198 238 277 255 190 188

(a) Run a one-way ANOVA followed by a Duncan’s multiple range test.

(b) Create a contrast to compare Placebo against the mean of Stain A and Stain B.

A well-known company manufactures combination locks. Their retractable cable lock works well for securing sports equipment (skis, bikes, golf equipment, etc.) as well as duffel or sports bags. A five-digit (0–9) dial combination lock secures the cable.

Suppose that you purchase one of these retractable cable locks to secure your bike to a bike rack at the library. How many five-digit combination lock codes are possible for your lock if you cannot repeat digits? Is this problem a combination or a permutation problem? Why?

In a poll of 1000 randomly selected prospective voters in a local election, 281 voters were in favor of a school bond measure.

a. What is the sample proportion? Type as: #.###

b. What is the margin of error for the 90% confidence level? Type as: #.###

c. What is the margin of error for the 95% confidence level? Type as: #.###

d. What is the 95% confidence interval? Type as: [#.###, #.###]

A poll reported a 36% approval rating for a politician with a margin of error of 1 percentage point.

a. How many voters must be sampled for a 90% confidence interval? Round up to the nearest whole number.

b. How many voters must be sampled for a 95% confidence interval? Round up to the nearest whole number.

Intelligence quotient (IQ) test scores are believed to have a mean of 100 and a population standard deviation of 15. In a random sample of 36 students in a high school, the mean IQ test score is 105. Researchers claim that the mean IQ test scores at this high school is statistically higher than 100.

a. What is the hypothesized mean?

b. Is the hypothesis test two-tailed, right-tailed, or left-tailed? Type as: two-tailed, left-tailed, or right-tailed

c. What is the z-score?

d. What is the p-value? Type as: #.#####

A transportation commission studies driving times between two cities to determine whether the construction of a new highway reduced commute times. Times for 40 cars driving on the old highway and times for 50 cars driving on the new highway are obtained. A summary of the data obtained from the study is given below.

a. What is the standard error? Type as: #.###

b. What is the z-score? Type as: #.###

c.What is the p-value? Type as: #.######

10,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and the control group is given a placebo. 95 of the 5,000 individuals in the treatment group developed a disease. 125 of the 5,000 individuals in the control group developed a particular disease. A research team wants to determine whether the vaccine is effective in decreasing the incidence of disease. Does sufficient evidence exist to conclude that the proportion of developing a disease in individuals given the vaccine is less than that of individuals given a placebo?

a. What is the proportion of individuals in the treatment group that developed the disease? Type as: #.###

b. What is the proportion of individuals in the control group that developed the disease? Type as: #.###

c. What is the proportion of individuals in the overall group that developed the disease? Type as: #.###

d. What is the standard error estimate? Type as: #.####

e. What is the z-score? Type as: #.###

f. What is the p-value? Type as: #.####

Let’s say you have an unfair six-sided die that lands on 2 exactly 20% of the time. If you roll this “loaded” die 5 times, what are the odds that you: (a) never roll a 2, (b) roll a 2 two times, or (c) roll a 2 more than two times? (use excel and show functions)

Consider the quarterly electricity production for years 1-4:

Year 1      2         3            4
Q1   99   120     139        160
Q2   88   108     127        148
Q3   93   111     131        150
Q4 111   130     152        170

(a) Using a classical additive decomposition, calculate the seasonal component.
(b) Explain how you handled the end points.
(c)  Estimate the trend using a centered moving average.

An experimenter is investigating the effects of noise on the performance of a tracking task. The task is to use a mouse to keep a cursor on a computer screen on a randomly moving target dot. The dependent variable is the amount of time a person can keep the cursor on the dot. It was hypothesized that subjects performing the task when no environmental noise is present will keep the cursor on the target for a greater amount of time than subjects who perform the task while listening to loud noise.

Each action by the experimenter that is described next confounds this experiment by letting an extraneous variable vary systematically with the independent variable of noise condition. For each action, identify the extraneous variable confounding the experiment and explain why the experiment is confounded.