Module #5 Assignment

 1.

A. H0= There is no evidence to suggest a statistically significant difference in the weight of cookies being manufactured compared to their specifications

     H1= There is evidence to suggest a statistically significant difference in the weight of the cookies being manufactured compared to their specifications

B. There is not evidence to suggest that the machine is not meeting the specifications.

C. A hypothesis test confirms this, as demonstrated below through the use of R. When compared using an alpha value of 0.05, the p-value (0.1870131) presents the conclusion that there is no statistical evidence to imply a fault in the machines consistency. 

D. Had the standard deviation been 1.75 rather than 3.2, the result would be different. Instead of receiving a p-value significantly above the 0.05 alpha value, the p-value would be 0.05368654, or 0.053 when truncated to 3 significant figures. This number falls slightly outside of the alpha range, implying that the null hypothesis must be accepted, however there exists some flexibility when considered the variance and room for error (+|-).

E. Had the conditions for the test been using a mean of 69 and an sdx of 3.5 pounds, the results would be more explicitly in support of the null hypothesis. The increase in variance from the standard deviation does not do much to enhance the statistical evidence in support of the alternative hypothesis. Under these circumstances, the p-value would instead be 0.2091732 (or 0.209 to 3sf), placing the alpha value significantly out of range. 

2. The z-value is 84.05

3.

Module 4, Assignment 4

 A. For this part of the assignment, I was confused because I did not understand what the table was supposed to be or what to do with it. At first I thought the numbers were probabilities, however due to the lack of a decimal sign or percentage to indicate it, I was somewhat confused. I somehow got 90, and input 30 for both A and B. 

A1. P(A) = 30/90 or 0.333

A2. P(B) = 30/90 or 0.333

A3. P(A or B) = 1/3 or 0.333

A4. 0.666

B1. False.

B2. The calculations are incorrect. It fails to describe the fact that the weatherman correctly predicts the rain 4.5/5 times a year, and incorrectly predicted rain 36.5/365 times a year. 4.5/5 times did the weatherman claim there was going to be rain and there was, in contrast to the 1/10 times that he said there was going to be rain and there was not. This ratio suggests that there is a higher likelihood that there will be rain for the wedding.

C.I have no clue how to use dbinom, or what the first xxx is supposed to describe within this question. 8/10 would likely have presented with no post-op complications after the traditional method was used.

Module 3, Assignment 3

This assignment was designed to show descriptive statistics using R programming. Using two sets of data, I was expected to run R to calculate the mean, median, and mode; the standard deviation (sdx), interquartile range (IQR), and the range. Using the provided format, I calculated the following:

Set 1: 10,2,3,2,4,2,5

Mean=4                                        Range=8

Median=3                                     IQR=3

Mode=2                                        Sdx=3.8444

Set 2: 20,12,13,12,14,12,15

Mean=14                                   Range=8

Median=13                                 IQR=3

Mode=12                                    Sdx=2.886751

The data sets contain a few similar characteristics. Either share an interquartile range and range. However the besides these there are no obvious similarities between the sets. Judging by the calculated Sdx's, the standard deviation for the first set is larger, meaning that the curve will be shifted more left than set 2. 

 For this assignment, the functions being evaluated were assignment2<- c(6,18,14,22,27,17,22,20,22) and myMean <- function(assignment2) {return(sum(assignment2)/length(assignment2))}.

The expectations for this assignment were to use the data set from the function assignment2 to return the mean value. I was unsuccessful in running this calculation using R, however I understand completely how and why the code outlined here is designed to run. Writing out assignment 2 using this format initializes the value for the function; assignment2= the values listed within the parentheses. I'm not sure why it's called myMean or if it serves a different purpose than simply "mean", but this function is designed to calculate the mean of the input vector (assignment2). By using 'function' this inputs the integers from the data set as the values for the calculations; the sum of the dataset(assignment2) divided by the length (number of entries within the data set) returns the mean. I'm still figuring out what went wrong during my attempts to fulfill this task, I spent multiple hours combing through videos and the textbooks to get a grasp on the introductory materials and still failed to run this code.