The table 1 below shows a relationship between actual daily temperatures and precipitation in the month of January 2011. These data was adopted from a meterological station in the states of Alaska, in the United States. Normal distributed data aresymmetric with a single bell shaped peaks. Th maean of the data it significant in indication the point that the peak is likely to occur. In addition, standard deviation indicates the spread, which is usually referred to asthegirth of thebeell shapedcurve (Balakrishnan & Nevzorov, 2003). Table 1: Relationship between actual daily temperatures and precipitation of January 2011 Date Actual Temperatures Precipitation  Jan. 1 30 0  Jan. 2 25 0  Jan. 3 31 0  Jan. 4 33 0  Jan. 5 29 0  Jan. 6 36 0.26  Jan. 7 36 0  Jan. 8 37 0.01  Jan. 9 32 0.21  Jan. 10 28 0.02  Jan. 11 43 0  Jan. 12 37 0  Jan. 13 36 0  Jan. 14 37 0  Jan. 15 34 0.02  Jan. 16 41 0.05  Jan. 17 40 0...
... standard deviation, variance, standard error of the mean, and confidence intervals. These statistics are used to summarize data and provide information about the sample from which the data were drawn and the accuracy with which the sample represents the population of interest. The mean, median, and mode are measurements of the “central tendency” of the data. The range, standard deviation, variance, standard error of the mean, and confidence intervals provide information about the “dispersion” or variability of the data about the measurements of central tendency.
MEASUREMENTS OF CENTRAL TENDENCY The appropriateness of using the mean, median, or mode in data analysis is dependent upon the nature of the data set and its distribution (normal vs nonnormal). The mean (denoted by x) is calculated by dividing the sum of the individual data points (where Σ equals “sum of”) by the number of observations (denoted by n). It is the arithmetic average of the observations and is used to describe the center of a data set.
mean=x= One of the most basic purposes of statistics is simply to enable us to make sense of large numbers. For example, if you want to know how the students in your school are doing in the statewide achievement test, and somebody gives you a list of all 600 of their scores, that’s useless. This everyday problem is even more obvious and staggering when you’re dealing, let’s say, with the population data for the nation....
...time is known to have a skewedright distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is skewedright with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is skewedright with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. d) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. ANSWER: c 2. Suppose the ages of students in Statistics 101 follow a skewedright distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? a) The mean of the sampling distribution is equal to 23 years. b) The standard deviation of the sampling distribution is equal to 3 years. c) The shape of the sampling distribution is approximately normal. d) The standard error of the sampling distribution is equal to 0.3 years. ANSWER: b 3....
...On Asymptotic Distribution Of Likelihood
Ratio Test Statistic When Parameters Lie On
The Boundary
A Project Submitted To The Department Of Statistics
University Of Kalyani, For Fulfillment Of M.SC 4th Semester
Degree In Statistics.
Submitted by
Suvo Chatterjee
Under the supervision of
Dr. Sisir Kr. Samanta
Department Of Statistics
UNIVERSITY OF KALYANI
Kalyani741235
DECLARATION
I , Suvo Chatterjee , a M.SC student of department of statistics , university of
kalyani hereby declare that my project entitled “On Asymptotic Distribution Of
Likelihood Ratio Test Statistic When Parameters Lie On The Boundary” has
been completed by me as a part of my M.SC examinations under the
supervision of Dr. Sisir Samanta department of statistics , university of kalyani.
This work has not been published elsewhere.
Date: 3072012...
...require that we know whether we have a sample or a population. 2. The following numbers represent the weights in pounds of six 7year old children in Mrs. Jones' 2nd grade class. {25, 60, 51, 47, 49, 45} Find the mean; median; mode; range; quartiles; variance; standard deviation. Solution: mean = 46.166.... median = 48 mode does not exist range = 35 Q1 = 45 Q2 = median = 48 Q3 = 51 variance = 112.1396 standard deviation =10.59 3. If the variance is 846, what is the standard deviation? Solution: standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6      219200 48714 0197 6
This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot?
45 40 35 30 25 20 15 10 5 0 0 5 10 15 20
Solution: Weak positive linear correlation 6. What values can r take in linear regression? Select 4 values in this interval and describe how they would be interpreted. Solution: the values are between –1 and +1 inclusive. 1 means strong negative correlation +1 means strong positive correlation 0 means no correlation .5 means moderate positive correlation etc. 7. Does correlation imply causation? Solution: No.
8. What do we call the r value. Solution: The correlation coefficient....
...hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normaldistribution.
a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
z(29) = (2932)/2 = 3/2
z(34) = (3432)/2 = 1
z(32) = 0
P(32 < x < 34) = P(0< z < 1) = 0.34
b. What percent of the garages take between 29 hours and 34 hours to erect?
P(29 < x < 34) = P(1.5 < z < 1) = 0.7745
c. What percent of the garages take 28.7 hours or less to erect?
z(28.7) = (28.732)/2 = 3.3
P(0 < x < 28.7) = P (10 < z < 3.3) = 0.00048348...
d. Of the garages, 5 percent take how many hours or more to erect?
find the zvalue corresponding to an area of 95% to the left and only
5% to the right under the curve.
Use your zchart or InvNor(0.95) = 1.645 on your calculator.
Now find the xvalue corresponding to that zvalue.
1.645 = (x32)/2
x32 = 2*1.645
x= 35.29 hours
5% of the houses require 35.29 or more hours to erect.
Chapter 8 #21
What is a sampling error?
Sampling error is the expected chance difference, variation, or deviation between a random sample and the population.
Chapter 8 #34
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normaldistribution with a standard deviation of...
...standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)
(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)
(c) What is the probability that [pic] will differ from the population mean by more than 0.7? (5 points)
4. In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds with a standard deviation of 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is taken:
(a) What is the mean and standard deviation of the [pic] = sample mean distribution? Can we assume the [pic] distribution is normal? Explain. (10 points)
(b) What average weights of for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds? (5 points)
(c) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (5 points)
5. A random sample is to be selected from a population that has a proportion of...
...
STAT 200
Section 7983
Sping 2012
`
Quiz #2
Please answer all 6 big questions. The maximum score for each question is posted at the beginning of the question, and the maximum score for the quiz is 60 points. Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with necessary tables, if applicable. Answers that come straight from program software packages will not be accepted. The quiz is due by midnight, Sunday, April 22, at 11:59 pm.
IMPORTANT: You are requested to include a brief note at the beginning of your submitted quiz, confirming that your work is your own. The note should say, "I have completed this assignment myself, working independently and not consulting anyone." Your submitted quiz will be accepted only if you have included this statement.
I have completed this assignment myself, working independently and not consulting anyone.
1. John made an experiment by tossing three fair coins. (Fair coin has the same probability for a tail and head ½).
(a) (3 points) List the sample space for this experiment. (All possible outcomes)
HHH, TTT, HTH, THT, TTH, HHT, HTT, THH = 8
(b)(2 point) What is a probability of three tails?
P(TTT) = 1/8 = 0.125
(c) (2 points) What is a probability of exactly two tails?
P(2 Tails) = 3/8 = 0.375
(d) (2 points) What is a probability of at least one tail?
P(1...
...
5. A score that is likely to fall into the middle 68% of scores of a normaldistribution will fall inside these values: (Points : 1) 
. +/ 3 standard deviations
+/ 2 standard deviations
+/ 1 standard deviation
semiquartile range

6. It is important to assess the magnitude or strength of a relationship because this assists you with deciding whether or not a variable A causes variable B. (Points : 1) 
True
False

7. In a negative relationship, as the score of one variable decreases, the score on the second variable decreases. (Points : 1) 
True
False

8. A set of subjects, usually randomly sampled, selected to participate in a research study is called: (Points : 1) 
Population
Sample
Mode Group
Partial Selection

9. A perfect negative relationship between two variables is expressed as r=0. (Points : 1) 
True
False

10. When examining the relationship between a nominal variable and an interval or ratio variable, you would create a table using the nominal variables, calculate the mode and median of the interval or ratio variable, then make a decision regarding the relationship using the mode and median. (Points : 1) 
True
False

11. A Z score of +/1.96 is equivalent to these values on a normaldistribution. (Points : 1)...