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Statistical Sciences 1024A/B Lecture Notes - Lecture 23: Central Limit Theorem, Multistage Sampling, Simple Random Sample

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graytortoise911
10 Nov 2018
School
Western University
Department
Statistical Sciences
Course
Statistical Sciences 1024A/B
Professor
John Thompson

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Document Summary

Con dence interval when x is random distributed o: In repeated sampling from the same population, a percentage c of the con dence intervals calculated contain the true parameter. Of the intervals you calculate, c% of them will contain the true parameter. Margin of error: refers to the error bounds due to random sampling. As z* increases= the margin of error increases. As individual observations become more variable (ie. o increases)= margin of error increases. As sample size n increases= margin of error increases. Need the assumption of a simple random sample or the data can be plausibly thought of as observations taken at random from a population. Data is collected badly with a selection bias of unknown effect (no valid con dence interval) Data is obtained by strati ed or multistage sampling (current formula is invalid but con dence intervals can be obtained that are of a different form) Caution: sample size and distribution of the observations.

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Related Questions

Which of the following is NOT true when testing a claim about a​proportion?

A. If you want to test a claim about population​ proportions, use the​ P-value method or the classical method of hypothesis testing.

B. When testing claims about population​ proportions, the traditional method and the​ P-value method are equivalent in the sense that they always yield the same result.

C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

D. Both the traditional method and​ P-value method use the same standard deviation based on the claimed proportion​ p, but the confidence interval uses an estimated standard deviation based on the sample proportion ModifyingAbove p with caretp.

9. Write a method with the following header public static void replace (String oldFile, string newfile, char oldChar, char newChar) throws IOException This method opens the file whose name is given by the String parameter oldFile (the input file) for reading, and opens the file whose name is given by the string parameter newlile (the output file) for writing. It then reads every lime in the input file. For each line, it creates a new line identical to the original line, creept for the fact that all occurrences of char oldchar in the original String have been replaced by occurrences of char newchar in the new line. When the new line has been properly created, it write it to the output file. Once all the lines in the input file have been read and a corresponding line has been written to the output file, the method clases both files. Additional notes: • You MAY assume that none of the parameters this method accepts are null; in other words, your method does not have to handle the case where one or more of the parameters are null. You MAY assume that all the 10-related classes have already heen imported properly . Finally, because the replace() method is specified to throw an exception object of type TORxception, you MAY assume that I/O related problems will occur while reading from the input file or writing to the output file. In other words, your method DOES NOT have to check that no such problems occur, and DOES NOT have to manage Texceptions using try-catch blocks. WRITE YOUR replace() METHOD IN THE SPACE BELOW: YOUR replace() METHOD CONTINUED: USE THIS PAGE IF YOU NEED ADDITIONAL SPACE. CLEARLY INDICATE WHICH QUESTION(S) YOU ARE ANSWERING HERE. USE THIS PAGE IF YOU NEED MORE ADDITIONAL SPACE. CLEARLY INDICATE WHICH QUES- TION(S) YOU ARE ANSWERING HERE. • String (package java.lang) Methods: - public String chal wale Al t ri g od med in the chance au - public int length(): R e ach of the string - public char chattin R echar w heefd index public chart to Chachay: Consthis String to a new c r y - public boolean equals Object anbject): Ce this string to and yect - public boolean equalsigmoce Case String anotherstring]: Cam p ing sider this String to anotherString - public int compareToString anotherString: Compare this String to anotherstring graphically returns a negative ef this string before anotherstring, apithe value of this Stringatering distries publie iw paneelgoro (String another Camp i ng Garden ces, string to anoth i ng li hically returns te value of this thing care anotherstring, apie as if this string e r anotherstring, Strings - public int indexin ch Rather within this string of the och ch-lil does not - public int index fint.ch, int from index): Returns the index within this string of the first Roe of character ch, starting the search at position from Index retums - 1 il ch does not in this String - public int indexor (String ste): Returns the index within this string of the first currence of ringt-d eur - public int indexOf(stringate, int from index): Resures the index within the string of the fare currence of shariaparting police froiden liste des not count i ng - public String subat ring it begintndax) Rema new string which is a webstring of this string compend of the chesting at position begintndex (inclusive) - puble string subat ring intaginindex intendindex: Returns a new sering that waring of this string, composed of the characters starting at position beginIndex (inclusive, and ending at - public String replace(char oldChar, char newchar): Returns a new string resulting from replacing a Tences of olchar in this string with new Char. puble string tolon Case(): Returns a new string consisting of all the characters in this sting - publle ting toppe : Roum ingiting of all the c on in this thing uverted to perce - publie ting tet): Returns a copy of this line with leading and wailing whitespace • Scanner (package java.util) Methods: - publie danner File source) thrown jatorio Foundation sa Scanner the fun the specified file - public scanner InputStream source): Cits Scanner that process and from the input stream - puble Scannerstag source): Corsa ww Scanner that produces wales w ed from the specified String -puble vold close(): Cwes this Scanner -puble boolean asext(): Return this can het in its input puble boolean asext.Double(): Return to the taken in this season al ante pasadala w ith Doble() ed publie boolean hat Into: Reutte le inse gule ed wat w eet Int() had - public boolean hati : Return true if this w ee - puble boolean has longt) Return true if the r in this cannerm ane das along the next long) with puble ting at the t e rm from the canner puble double Smerthea ter puble intention there the l ot. puble w ith the need them - puble Intolog m u long • Printstream ( kape Java.io) Methods: a - Pri le rlle) throw alo.Pilo t Pelat ihan the p rile - Printing the throw r alo. Pet Stichw e d the wind - le void lose them - le void phone boolean ve - void prichar public void print chart 6): the way of char public void print double d o uble bed, public void print (int ) Fins int value - public void printet a n net public void printing : Strings - public void printin (1 Tm the line by writing the line para ring - public void printinhoolna ) Prints hoolean when thinorminates the public void printin (cthar c h ar wheelthening the line public void print in char i ta way of cars and then the line public void print in double d in double valued and the terminates the line public void printin(int 1) Pints int value and then into the line public void printin ( jat ova t terminates the line pulle void print intring): Tits Strings then to the line Note that the printwriter class defines the same methods and constructors (except for the fact that the structors are called Print.writer instead of PrintStream) • Math (package java.lang) Methods: - please le podle double bear the value of a t the of - puble balle blanche a Returns they u se of dele with pe r than realto - pietate double random Ruma doble 0.0 wi th .. puble stat la doble sin double a: Rethe puble statie doble con double a Return ther l e, where a ininin we angle, wherea in in e -puble statie doble tan double a) R he i ngold , whereas o m public statie double toeges double agrad): C a ngrad v ideo puble salle de anable and we a r e - - estatie delle au t olewa idle de ahholooble • Character (packape java.lang) Methods: - public static boolean ibigit charch: D i chtechisadil public static int digit(charch, int radix: Return the meal of cho ch in the di radix-lich des representa digit - public statie char forbigit chat digit, ut radix) Rems the character of digit in the disa - public statie boolean isletter charch): Demines if character chalet publle statie boolean islowerCase(char ch): Determines if character ch is a character - public static boolean ipparate(char eh): Determines ir ductes chinuppercase cura nd - publicatie boliwhip (arch Termine if character his white a intola - public static char tolowrane(char chevert hech to low - public static char tolpperCase(char ch): Covers Chococh topp • Array list (package java.util) Methods: - public ArrayList(): Create a new em ArrayList which contains clements of type - public int (1 : R m the number of clans in this list - public boolean isimpty(): Rens true if this in contains no elements - public boolean contains (object o): Return true if this lintutins el compr a re performed using the equals() method on - public int IndexOf(obj ): Returns the index of the first currence of elemento in this list, or lir this listes contain this element companies are performed wing the equals() method - publiek galimt in ): Returns the elementat position index in this list - publieket fint inde element): Replace the element at the position index in this list with the - puble honlanad a ): Appends the specifiedalent to the end of this list. - public void (int in aw e t the specified element the price index in this - publiek veint index): Remove the de s ition index in the list - publie hoolean remove(object a s the fir e of the president of this if it is p r epared wing the equals() methodno - public void clear(): Remes all of the elements from this • Vile (package java.io) Methods: - puble File(String pathname: Creates a File representing the file at the given pathane

  1. Given the following main program

    #main
    a = [5,2,9,6,3] doubleList(a) print a

    Implement the function named doubleList that takes one list argument and modifies the list so that each element in the list is doubled. The statement print(a) in the main program will then have to print [10,4,18,12,6]

  2. Given the following main program

    #main
    a = [5,2,9,6,3]
    b = reversedList(a) print b
    print a

    Implement the function named reversedList that takes one list argument and returns a list that contains the elements in the list argument in reverse order. The statement print(b) in the main program will then have to print [3,6,9,2,5]. The statement print(a) must print the original list [5,2,9,6,3] unaffected. This means your function should not modify the list argument.

  3. Given the following main program

    #main
    a = [5,2,9,6,3] reverseList(a) print a

    Implement the function named reverseList that takes one list argument and reverses the list so that the modified list contains the same elements in reverse order. The statement print(a) in the main program will then have to print [3,6,9,2,5]

  4. What is the return value of the functions doubleList, reversedList and reverseList in questions 1, 2, and 3 above?

  1. Given the following main program

    #main
    a = [5,2,9,6,3]
    b = evenElements(a) print b

    Implement the function named evenElements that takes one list argument and returns a list that contains the elements in the list argument that are even integers. The statement print(b) in the main program will then have to print [2,6]. What is the return value of the function? Your function should not modify the list argument.

  2. Given the following main program

    #main
    a = [5, 2, 9, 6, 3, 7, 19, 4, 8, 17, 21, 20, 15] removeOddElements(a)
    print a

    Implement the function named removeOddElements that takes one list argument and modifies the list so that all odd integers in the list are removed. The statement print(a) in the main program will then have to print [2,6,4,8,20]. What is the return value of the function?

  3. Part A
    #Main program A=[5,8,2,0,-5,3] n=-5
    answer = isFound(A, n) if answer == True:

    print "The integer is found in the list" else:

    print "The integer is not found in the list."

    Consider the main program shown above. Write a Python function named isFound that takes a list of integers and an integer as arguments and returns True if the integer is found in the list; otherwise it returns False.

    Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, you must write a loop to go through the elements of the list.

    Part B

    Give the following main program

page2image58001280 page2image58001664

#main
A = [5,2,9,6,3]
B = [2,4,3,9,7,1,6,5]
flag = isList1InList2(A, B) if flag:

print "The list", A, "is contained in the list", B else:

print "The list", A, "is not contained in the list", B

Implement the function named isList1InList2 that takes two list arguments and returns True if and only if each element of the first list argument are found in the second list argument; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, if you wish, you can use the function you wrote in Part A.

For the lists shown in the main program, your function must return True because each element of list A is found in list B.

  1. A given List is known as Palindrome List if the reverse of the List contains the same elements in the same order of the original List. For example the List of integers [2, 5, 0, 3, 3, 0, 5, 2] is a Palindrome because the reverse of the List which is [2, 5, 0, 3, 3, 0, 5, 2] contains the same elements in the same order as the given List. However the List [1, 2, '2', 1] is not Palindrome because its reverse which is [1, '2', 2, 1] does not contain the same elements in the same order as the given List.

    Write a Python function named isPalindrome that takes a List as argument and returns True if the argument is a Palindrome List; otherwise it returns False. You don't need to write the main program; just write the function. If you would like to test your function, then it is ok to write the main program too but you will not get any mark for the main program.

  2. Given your function in question #7 above, what is the output of the following code: a=[]

    b = [5,2,9,6,3]

    print isList1InList2(a,b)

  3. Given your function in question #7 above, what is the output of the following code:

    a=[]
    b=[]
    print isList1InList2(a,b)

  4. Given your function in question #7 above, what is the output of the following code: a = [5,2,9,6,3]

    b=[]

print isList1InList2(a,b)

  1. Given the following main program

    #main
    a=[]
    n = readListElements(a)
    print "The user entered", n, "elements to the list" print a

    Implement the function named readListElements that takes one list argument and modifies the list by repeatedly asking the user to enter integer values and then appending them to the list. The process stops when the user enters -1000. The stopping value -1000 should not be appended to the list. Moreover your function must count the appended elements and return it. Example if the user enters the integers 31, -4, 9, 1,-1000 then your function must modify the list a to a = [31, -4, 9, 1] and return the number elements added which is 4.

  2. Write a function named createRandomList that takes an integer argument n and returns a list with n elements. The elements must be random numbers in the range [0,100]

  3. Given the following main program:

    #main

       n = int(input("How many elements do you want in your list? "))
   a = createList(n)
   s1 = sumOfElementsAtEvenIndexes(a)
   print s1

       s2 = sumOfElementsAtOddIndexes(a)
   print s2
   s3 = sumOfAllElements1(a)
   print s3

       s4 = sumOfEvenElements(a)
   print s4
   s5 = sumOfOddElements(a)
   print s5

       s6 = sumOfAllElements2(a)
   print s6
   if (s3 != s6):

             print "Something is wrong in your program."
   else:

             print "Looks like you have done a good job."

    Implement the functions as follows:

  •  createList: returns a list object with n elements. The elements are generated randomly so that each element is in the range [15,45]

  • sumOfElementsAtEvenIndexes: returns the sum of the elements at even indexes. Use a for loop or a while loop.

  • sumOfElementsAtOddIndexes: returns the sum of the elements at odd indexes. Use a for loop or a while loop.

  • sumOfAllElements_A: returns the sum of all the elements in the list using the functionssumOfElementsAtEvenIndexes and sumOfElementsAtOddIndexes. Here you are NOT allowed to use any loop; instead make function calls as described.

  • sumOfEvenElements: returns the sum of the even integer elements in the list. Use a for loop or a while loop.

  • sumOfOddElements: returns the sum of the odd integer elements in the list. Use a for loop or a while loop.

  • sumOfAllElementsB: returns the sum of all the elements in the list using the functions sumOfEvenElements and sumOfOddElements. Here you are NOT allowed to use any loop; instead make function calls as described.

17. Most data compression algorithms like winzip, gzip, lzip and etc are based on the frequency distribution of characters in a given string. Write a function named getFreqDistribution that takes a string argument and returns a LIST that has length 26 such that the first element of the list is the number of appearance of 'a' or 'A' in the string, the second element is number of appearance of 'b' or 'B', and so on so forth.

I'm studying python 2 and have a lot of troubles with solving these homework questions.