Dо peоple whо grow up with more cаts in the house thаn dogs become more of а cat person or a dog person? Below is a table of frequency counts from matched pairs of mothers and daughters from two discordant categories. Test the hypothesis that the following two proportions are the same: 1. The proportion of daughters who prefer cats and mothers who prefer dogs 2. The proportion of daughters who prefer dogs and mothers who prefer cats Mother prefers Dogs Mother prefers Cats Total Daughter prefers Dogs 15 19 34 Daughter prefers Cats 23 28 51 Total 38 47 85 a) Calculate the test statistic: [stat] (Type your answer to 3 decimals) Work/Technique Submission REQUIRED b) Using a confidence level of 95%, find the critical value: [critical] (Type your answer using rounding rules) Work/Technique Submission REQUIRED c) Find the P-value: [pee] (Type your answer using rounding rules) Work/Technique Submission REQUIRED d) Draw and label both a traditional and P-value graph Work/Technique Submission REQUIRED e) Determine if you should Reject or Fail to Reject : [reject] (Type the uppercase letter that matches the options below) A reject B fail to reject Work/Technique Submission REQUIRED f) Interpret your results Work/Technique Submission REQUIRED
C. The pоwer оf twоtime limit per test: 3 secondsmemory limit per test: 256 megаbytes Computer scientists reаlly enjoy powers of 2 (1, 2, 4, 8, ...), so hаving an array of powers of 2 can create some satisfaction around the USF campus. However, this satisfaction can be much greater if the array demonstrates the real power of two. One array can achieve that if every element in it can be added to another element of the array and form a power of 2. One example of such array is [1,3,5]. The element 1 can be paired with 3 to get 22=4, the element 3 can be paired with 1, and the element 5 can be paired with 3 to get 23=8. Thus, all elements in the array can be part of a pair that adds up to a power of 2, so it demonstrates the real power of two. Please note that an empty array also satisfy this condition. Given an input array, please determine what is the minimum number of elements that must be removed so that the resulting array demonstrates the real power of two. Input The first line contains the integer n (1≤n≤2·105) indicating the size of the array. The second line contains integers v1,v2,...,vn (1≤vi≤109) representing the elements of the array. Output Print the minimum number of elements needed to be removed from the given array in order to make it demonstrates the real power of two. Examples Input #1 Output #1 31 5 3 0 Input #2 Output #2 14 1 Input #3 Output #3 44 2 6 2 1