A Hypothesis is a claim about a population perimeter. By two type we can differentiate the hypothesis, one is null another one is Alternative hypothesis which will counteract the null hypothesis. An alternative hypothesis goes to opposite direction of null Hypothesis. We can differentiate the null hypothesis by “=” sign. The hypothesis will determine whether or not the test supports our statement. There is a non-rejection and rejection region which will indicate the limited area of the test value. if a value of a certain test falls in the rejection we can reject the null hypothesis but if the value falls in the non-rejection region then we can conclude that the null hypothesis cannot be rejected thus the test supports our hypothesis.
For the report we formed a group of 4 people and decided to take 40 sample to conduct multiple test to find out about the variables and queries regarding our report. In the case we took 4 types of variables: Gender, Age, Job and Salary. All of the samples were from NSU which included 30 male candidate and 10 female candidate. Genders were indicated with 0,1. Male referred to as ‘0’ whereas ‘1’ referred to female. The candidates were distinguished into 4 age groups, the candidates
1. aged below 18 were the 1st group,
2. 18-20 were the 2nd group,
3. the 3rd group were above 20 to 23 aged candidates,
4. the 4th and last group were the candidate who are aged above 23.
The number 1,2,3,4 in the age section on the data page indicated the discussed group numbers. After that the 3rd variable that were taken to conduct these tests was job. Whether or not the candidates were employed. ‘0’indicated that them as unemployed and ‘1’ indicated them as employed. The fourth section was occupied by variable salary with amount of how much they earn by employing themselves.
Samples were unbiased which will also be tested in the report. For our findings we used 4 different Models. ### Critical value approach: Critical value approach is the test where we test a sample to find out whether or not the test support our hypothesis by finding out the “Z” or “t” value from the designated table. If the value falls in the rejection region then we shall conclude that our hypothesis is rejected and if it is not the case then we conclude that our hypothesis is not rejected thus supports our hypothesis. ### Chi Square test A statistical test called a chi-square test is used to compare actual outcomes with predictions. This test aims to ascertain if a discrepancy between actual and predicted data is the result of random variation or a link between the variables you are researching.
The Anova test compares two kinds of variation: the variation within each sample as well as the variation between the sample means. The one-way Anova test statistics are represented by the formula F = MST/MSE. MST = SST/ p-1. .
A run is a sequence of one or more consecutive occurrences of the same outcome in a sequence of occurrences in which there are only two outcomes. The number of runs in a sequence is denoted by R. The value of R obtained for a sequence of outcomes for a sample gives the observed value of the test statistic for the runs test for randomness.Results and Discussions Critical value approach: Question: Find out if NSU students are aged above 25. [Male and Female]
Hypothesis: H0: μ=3(Age Group) H1: μ>3 Test statistic = 1.686 < t value=1.912 {Non Rejection region} The critical value for both the Male and female shows that it is less than 3. Which means for both cases the critical value falls under non rejection region. Which indicates that for both cases the students are below age 25. Meaning we can conclude that the test supports our Null Hypothesis. But the test has some drawbacks also such as the Value of alpha meaning there is chance of type-1 error. But we can confidently say that we run the test again and again 95% we shall come up with result such as this one. So, we are 95% confidence that the students of NSU is below age group-4 in other words below 25years. Question: Does Gender influence employment?
The table shows a statistically significant association between gender and employment status among students (\(χ^2~1~ = 4.93\), p = 0.026). This means that male students are more likely to be employed than female students. Specifically, the table shows that 1. 6 male students are employed, while 2. 24 male students are unemployed. This means that 20% of male students are employed. In contrast, 0 female students are employed, while 10 female students are unemployed. This means that 0% of female students are employed. R Markdown Referance