Hypothesis Testing and Type 1/2 Errors

This assignment provides a detailed solution to a hypothesis testing problem in business statistics. The student is given a population mean (μ) of 4.32, a sample mean (x̄) of 4.32, and a standard deviation (σ) of 4.32. They are asked to test the null hypothesis (H0) that the population mean is equal to the sample mean (H0: μ = μ), using a level of significance (α) of 0.05. The student calculates the test statistic (t) and compares it to the critical value (t crit) from a standard normal table, rejecting the null hypothesis if the absolute value of t is greater than t crit. In this case, the student rejects the null hypothesis, indicating that there is sufficient evidence to support the claim that the population mean is not equal to 4.32. The assignment also discusses type 1 and type 2 errors, with a type 1 error occurring when a true null hypothesis is rejected, and a type 2 error occurring when a false null hypothesis is failed to be rejected.

Running Head: HYPOTHESIS TESTING 1
Hypothesis Testing
Napoleon Wilson
South University
BUS7200 Statistic for Research Methods 1
Week 1 Project
Dr. List
September 27, 2020

HYPOTHESIS TESTING 2
Giving that the Population menu ( μ)= μ. The Standard Deviation, = 4.32
sample mean 1x =4.32, number (N) =100, Null, Ho: = μ
Alternate: H1 :m = μ , Level of Significance, x = 0.05
From standard normal table, two tailed 2 α\2 + 1.95996. Since our test is two- tailed
reject Ho 20< -1.95996 or 20>1.95996
I use test statistics (2) = x-u\cs*d\sqrt (n1)
20= 4.32- μ\(0.67\sqrt (100)
20= 6.78
1201=4.78
The value of 12 d\ at los 5% os 1.95996
(20) =4.78 & (2x) =1.95996
Make the decision:
Since the value of 20> 2x and right here, I have Ho
P-value: two tailed (double the one tail)-Ha (p!=4.78) =0
The value of Po.0>, He we reject Ho
My answer is made from this simple solution
Null, HO: M = μ, Alternate hypothesis: H1 : M! = μ, test statistic: 4.78
conditional value: -1.95996, 1.95996
decision reject HO
P-value : 0

HYPOTHESIS TESTING 3
I found enough evidence to support the claim that
Type 1 Errors happen when I reject a tone null hypothesis
Type 2 Errors happen when I fail to reject a false null hypothesis
So that in this content we reject the null hypothesis, that is type 1 error.

HYPOTHESIS TESTING 4
References
Orris, B.B.R.O.E.M.J. B. (2014). Essentials of Business Statistics. [South University].
Retrieved
from https://digitalbookshelf.southuniversity.edu/#/books/1260089932/