Please answer all the question. I will rate you. Thanks

I am creating a design and plan project. about; Memorial Hospital Pembroke is making a serious effort to raise salaries for the Patient Care Assistant in the Human Services Department. Based on a recent news article from this specific area, the (mean) average salary for the PCA's is now $22, give or take $2, which represents the standard deviation. Tony, a rather new stats intern at the hospital put together a sample of the hourly wages for 30 PCA's with the sample mean hourly wage of $23. He is somewhat skeptical that the reported wages are at the reported level, but won't speculate if higher or lower than reported. Is the claim that the human services department's claim reasonable, at the 1% level of significance?

with the information above I need you to answer all the questions:

Question 1)

What is your research question stated symbolically as null and alternative hypotheses? Each hypothesis should be written symbolically and concisely with as few keystrokes as necessary to convey the conjectures.

Question 2)

Which type of test will be utilized for this testing: one-tail-left, one-tail-right, or two tail?(Justify the choice)

Question 3)

What level of significance will be utilized, for instance 1% or 5%? If a non-standard alpha level is preferred or appropriate, please explain.

Question 4)

Determine the one or two critical values, rounded to the nearest thousandth.

Question 5)

Make a reasonable estimation of the range of the population you are studying. Your best guess is acceptable as a worst-case scenario.

Question 6)

Utilize the range rule, where the range is divided by four, to estimate the population standard deviation.

Question 7)

What error bound is reasonable and appropriate? Express your answer in the same units as the population mean you are conjecturing. For instance, you want to be accurate to within five pizzas on how many are ordered on average on a Friday night at a single Domino's Pizza restaurant.

Question 8)

Calculate the minimum sample size for estimating a population mean, rounding up. Explain or justify this computation with a corresponding formula

Question 9)

Affirm that the data would be collected utilizing a sampling methodology, rather than simulation, survey or questionnaire, experiment, or census. A census isn't suitable because of the larger population and this is planned as inferential, not descriptive, statistical analysis.

Question 10)

What sampling technique will be utilized to create this sample? For example, will it be cluster, systematic, convenience, simple random, or one of the other choices? Explain your selection, and the logistics of how it would work in practical terms in no more than a few sentences.

Question 11)

State the technical conclusion, expressed as reject or fail to reject, if the test statistic generated from the sample mean taken from your planned sample is more extreme than the critical value.

Question 12)

State the contextual conclusion, expressed as reasonable or unreasonable, if the test statistic generated from the sample mean taken from your planned sample is more extreme than the critical value.

Question 13)

State whether or not the finding as reported in Items #12 & #13 is statistically significant.