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Multiple Statistics problems, homework help

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Attached are the five problems i am having difficulty on from my homework, each problem has sub questions Example here is the first problem and sub questions

1. 
When major league baseball scouts measured the
pitching speeds (in MPH) of 14 professional baseball prospects, they obtained
the results given by the data set, D = {92, 88, 85, 95, 91, 90, 84, 96, 89, 94,
86, 89, 90, 81}. Assume the population standard deviation is σ = 4.13, use a
significance level, α = 0.05, to test the claim that the mean pitching speed of
prospects is less than 90 MPH.

a.  Identify the null hypothesis and
alternative hypothesis

b.   Find the test statistic

c.  Identify the P-value

d.  What is the final conclusion?

1.  Fail to reject H0. There is not sufficient
evidence to support the claim.

2.  Reject H0. There is sufficient evidence to
support the claim.

3.  Reject H0. There is not sufficient evidence
to support the claim.

4.  Fail to reject H0. There is sufficient
evidence to support the claim.


the steps for each one (problem and sub questions)  would most certainly help me understand each problem better and are required. Each question is needed to be answered 5 in total to include the sub problems attached for a total of 21.  I’m at a loss for where to begin.

Thank you so much for your time

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