[Initial post requirements]

Describe a hypothesis test that you would like to conduct. Be sure to include the null and alternate hypotheses as well as the data you would need to collect to conduct the test. Discuss which level of significance you would use and why you would use that level. Further explain what you would do if you obtained a test statistic that was equal to the critical value.

[Respond to these classmates]

For this forum discussion, the percentage of Service Members that received their yellow fever vaccination is analyzed. A Brigade Commander – in a meeting – asked one of his subordinate Commanders the following question: “What is the % of Service Members vaccinated with yellow fever, is it above of my directed 90%?” The Commander, not having the information on hands and wanting to impress his superior, made a guess and told him, “Sir, we are currently on 95%.” (Attention, this story is fictional, although it looks real but is just for the intent of the class).
The Brigade Commander directed that 90% of his troops needed to be vaccinated with yellow fever for future deployments and countries requiring such vaccination.
95% was the estimate/guess of the Commander to his superior.
There are approximately 192 Service Members in that Company.
Four (4) squads from different platoons trying to build camaraderie were passing by marching en route to the dining facility. The Commander and First Sergeant stopped them and asked their leader to make accountability and by hand advise if they got their yellow fever vaccination.
39 out of the 48 Soldiers were vaccinated correctly. This is 81.25% of that sample population.
So, this project’s level of significance would be 95 %, giving us a 5 percent margin of wrong. The Commander said 95%, but the Brigade Commander said he wanted 90%. We are mostly trying to be within the stipulated guidance of 5 % guess-estimate.
H0: Mean = 90% of troops vaccinated with yellow fever. Fail to reject.
HA: Mean not equal to 90% of troops vaccinated with yellow fever. Reject or accept?
By default, the Z Score for 95% confidence interval is 1.96, and the confidence interval for this project was 0.114534244. So, 0.1145 is less than 1.96, and the Commander’s guess was incorrect. Fail to reject the null hypothesis to prove that 90% or more of the Service Members were vaccinated.
If a critical value is less or equal to the alpha value, then it has statistical significance. If it is more, then the alternate hypothesis becomes accepted, and we could fail to reject the null hypothesis.

Since I have recently spent some time looking for a monthly rental in Jacksonville Florida, I would like to do a hypothesis test on monthly rentals for a 3-bedroom house in Jacksonville. Our realtor stated the average rent for this size house in Jacksonville is $1000. We drove around the area and sampled 10 random rental homes in which we found that the average rent was $900 monthly with a standard deviation of $20. So, I am claiming the rent is less than the average rent in Jacksonville. In this case the following data will be used to develop my two hypotheses, calculate the t value and the critical value of the data. Formulas retrieved from text. Alexander, Illowsky, & Dean (2017)

Data:

m= 1000, n= 10, x= 900, s= 20, a = .05

.05 level of significance because this number indicates a 5% risk that a difference exists if there is no real difference in results.

Null Hypothesis: H0: μ =1000

Alternative Hypothesis: Ha: μ <1000

Distribution of test statistics:

t = (X – H0)/(n/square root of s)

t= (900 -1000)/(10/ 4.47) = -2.237

Critical Value:

n-1= 9 degree of freedom

Critical value -1.833

After reviewing all of this data you will see that my critical value of -1.833 is greater than the t value of -2.237, so this means that we fail to reject the null hypothesis. If you obtained a test statistic that was equal to the critical value, the same thing would happen and we would fail to reject the null hypothesis.

References

Alexander, H., Illowsky, B., & Dean, S. (2017). Introductory Business Statistics. Openstax. Retrieved from https://openstax.org/details/books/introductory-bu…