Question

In: Statistics and Probability

Consider Dataset C for answering the questions that follows below. Team Gender Responses 1 A Male...

  1. Consider Dataset C for answering the questions that follows below.

    Team

    Gender

    Responses

    1

    A

    Male

    3.25

    2

    A

    Male

    3.54

    3

    A

    Male

    1.08

    4

    A

    Male

    2.14

    5

    A

    Male

    3.60

    6

    B

    Male

    4.36

    7

    B

    Male

    4.66

    8

    B

    Male

    1.52

    9

    B

    Male

    3.99

    10

    B

    Male

    3.60

    11

    C

    Female

    3.86

    12

    C

    Female

    4.89

    13

    C

    Female

    1.46

    14

    C

    Female

    4.74

    15

    C

    Female

    4.16

    1. Teams A, B and C have been used to serve as respondents in a recently concluded webinar in Cybercrime to evaluate the delivery of the webinar. Is there any reason to believe that the mean responses of the three teams are different from one another? Test this using a level of significance of 0.05.
    1. All the teams are being categorized as either Male or Female. In this scenario, can we say that the mean male responses is different from the mean female responses? Test this claim at 0.01 level of significance.

Solutions

Expert Solution

A B C
count, ni = 5 5 5
mean , x̅ i = 2.722 3.63 3.82
std. dev., si = 1.090 1.243 1.385
sample variances, si^2 = 1.188 1.544 1.920
total sum 13.61 18.13 19.11 50.85 (grand sum)
grand mean , x̅̅ = Σni*x̅i/Σni =   3.39
square of deviation of sample mean from grand mean,( x̅ - x̅̅)² 0.446 0.056 0.187
TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² = 2.231 0.278 0.933 3.44272
SS(within ) = SSW = Σ(n-1)s² = 4.754 6.176 7.678 18.6081

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    1.7214
  
mean square within groups , MSW = SSW/N-k =    1.5507
  
F-stat = MSB/MSW =    1.1101

SS df MS F p-value F-critical
Between: 3.44 2 1.72 1.11 0.3611 3.89
Within: 18.61 12 1.55
Total: 22.05 14
α = 0.05
conclusion : p-value>α , do not reject null hypothesis    


Ho: µ1=µ2=µ3
H1: not all means are equal

We can conclude that all means are equal

b)

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.01                  
                          
Sample #1   ---->   Male
mean of sample 1,    x̅1=   3.17                  
standard deviation of sample 1,   s1 =    1.20                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   Female
mean of sample 2,    x̅2=   3.82                  
standard deviation of sample 2,   s2 =    1.39                  
size of sample 2,    n2=   5                  
                          
difference in sample means =    x̅1-x̅2 =    3.1740   -   3.8   =   -0.65  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    N/A                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.7267                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -0.6480   -   0   ) /    0.73   =   -0.892
                          
Degree of freedom, DF=   n1+n2-2 =    7                  
t-critical value , t* =        3.4995   (excel formula =t.inv(α/2,df)              
Decision:   | t-stat | < | critical value |, so, Do not Reject Ho                      
p-value =        0.402144   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value>α , Do not reject null hypothesis                      
                          
There is not enough evidence that male mean is different than femal mean

Thanks in advance!

revert back for doubt

Please upvote



Related Solutions

Consider Dataset C for answering the questions that follows below. Teams A, B and C have...
Consider Dataset C for answering the questions that follows below. Teams A, B and C have been used to serve as respondents in a recently concluded webinar in Cybercrime to evaluate the delivery of the webinar. Is there any reason to believe that the mean responses of the three teams are different from one another? Test this using a level of significance of 0.05. All the teams are being categorized as either Male or Female. In this scenario, can we...
Consider Dataset A for answering the questions that follows below. a. Calculate the measures of central...
Consider Dataset A for answering the questions that follows below. a. Calculate the measures of central tendencies for Variable X and Variable Y. i. Mean ii. Median iii. Mode iv. Midrange v. What can you say about the skewness of X and Y variables? b. Calculate the measures of variations for Variable X and Variable Y. i. Range ii. Variance iii. Standard Deviation iv. Coefficient of Variation v. Which is more variable, X or Y? Why? c. Calculate the measures...
Consider Dataset D for answering the questions that follows below. The median marks for Course X...
Consider Dataset D for answering the questions that follows below. The median marks for Course X and Y for the past 8 semesters were given on the dataset. Determine the strength of relationship between Course X and Course Y by calculating the correlation coefficient between them. What can you say about their relationship? Calculate the regression line that best explain the relationship between the dependent variable Course Y and independent variable course X. Estimate the most likely value for Course...
Using R to solve these questions: 1.Consider the following dataset: fuel <- c(0.95, 0.52, 0.82, 0.89,...
Using R to solve these questions: 1.Consider the following dataset: fuel <- c(0.95, 0.52, 0.82, 0.89, 0.81) The numbers correspond to the amount of fuel burnt by a new type of high-efficiency engine under a randomised test load. A value of 1 corresponds to the same fuel efficiency as the old engine, values greater than one correspond to more fuel burned (hence lower efficiency) and values less than one correspond to greater efficiency. (a) One-sided or two-sided test? Justify. (b)...
Using R to solve these questions: 1.Consider the following dataset: fuel <- c(0.95, 0.52, 0.82, 0.89,...
Using R to solve these questions: 1.Consider the following dataset: fuel <- c(0.95, 0.52, 0.82, 0.89, 0.81) The numbers correspond to the amount of fuel burnt by a new type of high-efficiency engine under a randomised test load. A value of 1 corresponds to the same fuel efficiency as the old engine, values greater than one correspond to more fuel burned (hence lower efficiency) and values less than one correspond to greater efficiency. (a) One-sided or two-sided test? Justify. (b)...
Review consumer choice by answering the following questions (a) through (c) below. Be thorough when labeling...
Review consumer choice by answering the following questions (a) through (c) below. Be thorough when labeling your graphical work. Values such as quantities and prices are not necessary. a)         Find the consumer’s equilibrium, E. Present the slopes of the budget constraint and the indifference curve at point E algebraically. b)         Find the new equilibrium, E1, caused by a decrease in the Px. c)         Find the income and substitution effects of this price change. Define the income and substitution effects.
Option #1: Lease Complete the following questions. In addition to answering the items below, you must...
Option #1: Lease Complete the following questions. In addition to answering the items below, you must submit an analysis of the assignment. Analyze the specific outcomes and write an analysis directed toward the team at Coco Inc. describing what the numbers mean and how they relate to the business. Submit journal entries in an Excel file and written segments in an MS Word document. For written answers, please make sure your responses are well-written, formatted per CSU-Global Guide to Writing...
Part 1. Consider the dataset below. You will perform a series of regressions and data transformations....
Part 1. Consider the dataset below. You will perform a series of regressions and data transformations. Be sure to keep a record of all your computer results. First, please perform a simple linear regression. Predict Y if X = 40. To avoid rounding errors in ALL your calculations, please perform your calculations on your spreadsheet referencing data from your regression output. X Y 54 6 42 16 28 33 38 18 25 41 70 3 48 10 41 14 20...
Consider the dataset shown below where the decision attribute is restaurant
Consider the dataset shown below where the decision attribute is restaurantShown below is a partially developed decision tree. Finish creating the tree using the ID3 method. YOU WILL NOT RECEIVE ANY CREDIT UNLESS YOU SHOW ALL OF YOUR WORK IN TERMS OF ENTROPY AND INFORMATION GAIN CALCULATIONS!!!
Using the Titanic passenger dataset (titanic.csv). Is it better to split on gender or Pclass (1...
Using the Titanic passenger dataset (titanic.csv). Is it better to split on gender or Pclass (1 or not 1)? Compute information gain for each option and say which is best. Submit the gain and show your work and your choice. - I cant upload the dataset on here. Can I send a link of it from google? What can I do?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT