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.

index	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
score	35	50	58	59	60	61	65	66	68	68	71	74	76	76	79	82	84	88	90	92	94	97

(a) The value of P₉₀ ---->

(b) Complete the 5-number summary.

Minimum	=	35
Q1	=	???
Q2	=	???
Q3	=	???
Maximum	=	97

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.

Highway	Mean commute times	Population standard deviation
1 (Old)	5.35	0.5
2 (New)	4.95	0.8

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.                                                                                   

3a. [1 point] The experimenter assigned ten 20-year-old males to the no-noise condition and ten 60-year-old females to the noise condition.

3b. [1 point] The experimenter urged the subjects in the no-noise condition to try very hard, but forgot to encourage the subjects in the noise condition.

3c. [1 point] Subjects in the no-noise condition performed the experiment at 9:00 A.M. and subjects in the noise condition performed the experiment at 4:00 P.M.

3d. [1 point] The experimenter let participants choose which group (no-noise or noise condition) they wanted to be assigned to.

Running times (Y) and maximal aerobic capacity (X) for 14 female
Runners. Data collected for running times and maximal aerobic capacity are listed below

X: 61.32 55.29 52.83 57.94 53.31 51.32 52.18 52.37 57.91 53.93 47.88 47.41 47.17 51.05

Y: 39.37 39.80 40.03 41.32 42.03 42.37 43.93 44.90 44.90 45.12 45.60 46.03      47.83 48.55

(a) Calculate the mean, median, MAD, MSD, and standard deviation for each variable. ? [Include all your steps and explain all the steps involved in details]
(b) Which of these statistics give a measure of the center of data and which give a measure of the spread of data?
(c) Calculate the correlation of the two variables and pro-duce a scatterplot of Y against X. [Use excel for scatterplot, show all your computations concerning the correlation and explain all your steps]
(d) Why is it inappropriate to calculate the autocorrelation of these data?

Econ 2310

Business Statistics: Problem Set #1

Instructions: You may use Excel and/or a calculator to complete this assignment. Please show work or reference what Excel commands you used to solve the problems.

1. You are given the following two series on income and credit scores.

Income	FICO
39	625
27	600
57	710
31	595
34	610
50	840
38	726
62	710
43	635
49	560

1. Find the covariance and the correlation coefficient. (B) Do credit scores increase, decrease, stay the same, with Income? (C) Create a scatter plot with Income and credit score. What do you see?

2. Suppose you flip a fair coin four time. (A) What is the probability you will get all four heads? (B) All four tails? (C) Either all four heads or four tails? (D) Anything but four heads or four tails?

3. Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.    

1. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
2. If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.

4. In the BS Lottery (which stands for “Business Statistics”, of course), players choose 5 numbers out of 30. They win if they choose the same 5 numbers as our machine, which selects the numbers randomly. (A) How many permutations are possible? (B) How many combinations are possible?

5. Below is a table of X and its frequency. What is the mean of X? What is the standard deviation of X? What is the variance of X?

X	Frequency
2	20%
5	10%
8	15%
10	30%
12	25%

A coin that lands on heads with a probability of p is tossed multiple times. Each toss is independent. X is the number of heads in the first m tosses and Y is the number of heads in the first n tosses. m and n are fixed integers where 0 < m < n. Find the joint distribution of X and Y.

The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 15 and 18 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 26.856 kg and 0.218 kg for machine 1 and 24.818 kg and 0.369 kg for machine 2. Hence, under the usual assumptions, determine a 95% confidence interval for the difference between the average weight of the output of machine 1 and machine 2. Use machine 1 minus machine 2, stating the upper limit of the interval correct to three decimal places.