Calculating error probability and test power.

Calculating probability of Type II error, Power of the Test, and error test

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A construction firm thinks that it is receiving 100 steel pipes with an average tensile strength of 10,000 pounds per square inch(lbs p.s.i.).This is the mean,μ.The size of the sample was n=100.The firm also knows that the population standard deviation,sigma,σ,is 400 p.s.i.The firm chooses a confidence interval of 95 %.This is equivalent to a level of significance,α,of 5 %(.05),where the null hypothesis is H₀:μ₀=10,000 and the alternative hypothesis is H₁:μ₀≠10,000.The company does not know that the actual, average tensile strength is not μ₀=10,000,but μ₁ =10,100.

Calculate the probability of making a Type II (β) error both graphically and quantitatively, the Power of the Test, error test.

A construction firm thinks that it is receiving 100 steel pipes with an average tensile strength of 10,000 pounds per square inch(lbs p.s.i.).This is the mean,μ.The size of the sample was n=100.The firm also knows that the population standard deviation,sigma,σ,is 400 p.s.i.The firm chooses a confidence interval of 95 %.This is equivalent to a level of significance,α,of 5 %(.05),where the null hypothesis is H₀:μ₀=10,000 and the alternative hypothesis is H₁:μ₀≠10,000.The company does not know that the actual, average tensile strength is not μ₀=10,000,but μ₁=9,940.Calculate the probability of making a Type II (β) error, the power of the Test, I error test.

Correlation(Part 1)- -compute r,r²and 1-r² for the problem below .What does r,r² and 1-r² mean ? Is the correlation strong or weak ?

X(Independent Variable) Y(Dependent variable)

Month Advertising Expenditure (in Millions of $) Sales Revenue (in Millions of $)

July 1 3

August 2 7

September 3 5

October 4 11

November 5 14

Correlation(Part 2)- Do a Hypothesis Test for the Correlation Coefficient ,r, that you calculated in the previous HW problem,Correlation(Part 1) .

Assume that you want to test for a positive correlation. Let α,your level of significance ,be .05.The number of observations, n, is 5.Use n-2 degrees of freedom. Do you reject or do not reject H₀ ?

You need to do the 6 steps for the Neymann-Pearson critical value test.You do not need to do a Fisher p-value test for the correlation coefficient ,r.

Regression (Part I)- You are again given the same 5 observations that you were provided with in the Correlation problem.However,you are now asked to derive the regression line,y’= a+bX for the data below.After you have calculated the regression equation,explain to me how you could use it.