Need correct approach for this statistics and probability question without using AI tool.

Do not use ChatGPT otherwise i will unhelpful need help in this statistics qn.

I need help in this statistics question without use chatgpt!

please give correct answer of this statistics and probability question.

Could you please help me answer parts b and c. Thanks

Suppose that we have data y = (1,...,n). Each data point y; is assumed to be generated by a distribution with the following probability density function: P(yi | n)=3nye, y; ≥0. The unknown parameter is >0. (a) Write down the likelihood for n given y, and find an expression for the maximum likelihood estimate (MLE) of n. (b) A Gamma(a, 3) distribution is chosen as the prior distribution for 7, where a > 0 and > 0 are known. Show that the posterior distribution of n, denoted p(n | A), is also a gamma distribution with updated parameters that you should determine.

Do the data provide compelling evidence (at α=0.05) for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade? Show all your work. Estimate the difference between true average strengths for the two grades with a 95% confidence interval for the previous problem.

Use Minitab and the GPA data (GPAData.xlsx) to answer the following. a) (15 points) Is there a mean difference in High School GPA and a person's GPA following their first year of college? State the relevant hypotheses and provide the p-value from the output. Include a decision and interpretation at a 10% level of significance. b) (5 points) Is the assumption of normality satisfied? Include any plots you make to check the normality assumption and comments on your observations.

A researcher wants to perform a hypothesis test to see if the mean salary of the faculty in private and public institutions are different. Random samples of 36 faculty from private and public institutions were selected. Salaries of the selected faculty from private and public institutions are provided to you in facultysalary.csv file. 1. Make side-by-side boxplots of the salaries for faculty in private and public institutions (In MINITAB, go to Graphs-- >Boxplot-->and explore the available options to see how to make a side-by-side boxplot of the data). 2. Comment on your observations from the side-by-side boxplot made in part 1. 3. Calculate the descriptive statistics: mean, standard deviation for the two samples and attach the MINITAB output. 4. When carrying out a hypothesis test to achieve the aforementioned goal, would you recommend using pooled variance approach or unpooled variance approach? Provide reasoning for your choice. 5. Regardless what you recommend in part 4, carry out…