I will attach an example for the legal memorandum.

MEMORANDUM

To: The Honorable Farah Hadi

CC: Tolford v. The Automotive Shaft Company

From: Student's name

Date: April 18, 2019

Subject: Critical comparison of opposing claims, analytical thinking, and problem-solving

Question Presented

1. Conduct the appropriate hypothesis test. Whose claim would you support?

2. What is the t -test outcomes?

3. What is the p - value?

4. What distribution used?

Brief Answer

1. Formulating the null and alternative hypotheses,                              Ho:   u   =   3.5   Ha:    u   >   3.5   As we can see, this is a right tailed test.       Getting the test statistic, as :        

The p-value for this one tailed test is computed as: ( for n-1 = 7 degrees of freedom )

The distribution used here would be t-distribution because we are given the sample standard deviation and not the population standard deviation.

Facts

The information used in this analysis are as follows:

amount of shaft wear = 0.0001in

n = 8

s = 1.25

μ = 3.50

sample mean = 3.72

Discussion

This analysis is to determine and evaluate if the population mean µ is greater than 3.50. To derive the answer, the calculation of p-value and the t-test, justifying wethere the the null hypothesis will be rejected or not with the utilization of significance level of 0.05. Since, t-tes and the p -value are accuae approcah to evalaute the hypothesis given. The outcome of the t-test is 0.498 ≤ tc = 1.895. The outcome for the p-value is 0.3169. These both outcomes from the applied analysis, it is concluded that the null hypothesis is not reject sine, the t-test outcome is greater than the significance level of 5%, same with the outomes of the p - value.

Counterargument

It was argued that the averages shaft wear has mean 3.50 larger the alternative hypothesis that the true mean is less than 3.5. Based on the information, the significance level provided, the significance level is argument is not valid, because given the result of t- tests is 1.895 which is higher than the given 5% of significance level used, therefore, the arguments is false or not valid.

Conclusion

It is concluded that the null hypothesis H0 is not rejected. Therefore, there is not enough evidence to claim that the population mean µ is greater than 3.50, at the significance level

of 0%.

Visual support

Figure 1: Probability Density function

Figure 2: Cumulative Distribution function

Addendum 1: Statistical Calculations

T - Test

P - value

p= P( t_7 > 0.4978 ) =  0.3169

Critical comparison of opposing claims, analytical thinking, and problem-solving 1