Description of how to write the null and alternate hypothesis based on a claim with an example
A hypothesis is an approximate, solely based on the chance that explains a characteristic of a given dataset and can be investigated using statistical techniques. There are two types of hypothesis, the null hypothesis, and alternate hypothesis. The null hypothesis is denoted as H 0 states the conventional expectation which is the exact opposite of a claim. Whereas, the alternate denoted as H a , is a statement that suggests that there is possible positive outcome out of the investigation backing the claim. Given the example below, the steps for writing the null hypothesis and alternate hypothesis will be as follows.
A certain factory installed an automatic metal peace cutting machine. The machine is supposed to cut 203mm long metal pieces. However, the workshop manager suspects that the machine could be cutting longer metal pieces. He decides to randomly take 50 samples and see if their average length is significantly longer than the expected.
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The null hypothesis will be set based on what is expected of the metal peace cutting machine. Meaning that for H 0, the mean will be equal to 203mm H 0 : σ = 203mm
The alternate hypothesis, on the other hand, will be set to concur with the claim. In essence, it depicts that the investigation will give results in statistical significance. In this case, H a, the average will be greater than 203mm H a : σ = 203mm.
σ is the mean of the 50 samples.
Question 2
Response on Alyson Davis
The definitions of both null hypothesis and the alternate hypothesis are right. Furthermore, the identification of the contradiction to the claim is accurate. Therefore, the constructed null and alternate hypothesis is constructed and explained correctly.
Response on Jemal Brown
The definition of null hypothesis is right. However, the definition of the alternate hypothesis is inaccurate on the part that states that "it includes all the possible values not included in the null hypothesis. The values included in the alternate hypothesis are guided by what is suspected. Furthermore the constructed null hypothesis is inaccurate the correct answer is H 0 : μ = 5 years.
Question 3
The Difference between the Standard Normal Distribution and Nonstandard Normal Distribution
The standard normal distribution is a normal distribution that has a mean of 0 and a standard deviation of one. Furthermore, 68% of the observations are within one standard deviation from the mean, 95% of the observation within two standard deviations and 99.9% within three standard deviations. On the other hand, the non-standard normal distribution has a mean value other than zero and a standard deviation value that is not 1.
How to Find Probabilities of a Non-Standard Normal Distribution
Convert the raw score to Z score using the formula Z = (x- μ)/ σ where x is the raw score, σ is the standard deviation and μ is the mean.
Use the standard normal distribution table to find the probability.
Non- standard normal distribution differs from the standard normal distribution. Describe the process for finding probabilities for nonstandard normal distributions
Question 4
The Relationship between the Linear Correlation Coefficient and the Usefulness of the Regression Equation for Making Prediction
Both linear correlation coefficient and the regression equation are a measure of the relationship between two variables. However the regression coefficient goes further to designate the variable into dependent and independent. Furthermore, it states the capability of predictability. They are useful in prediction because they add a mathematical formula to enhance the precision of the prediction.
