The final questions test your understanding of hypothesis testing in the context of the triangle taste test we discussed in class.In this case, the test consists of 15 identical trials on which the subject (a job applicant) attempts to identify the odd sample on each trial, and H₀: p = 1/3 and H_a: p > 1/3. Assume the 2 rejection regions are: (1) R₇ = {7, 8, 9, 10, 11, 12, 13, 14, 15} and (2) R₉ = {9, 10, 11, 12, 13, 14, 15}.

1.For R₇ = {7, 8, 9, 10, 11, 12, 13, 14, 15}, what is the probability of a Type I error? ____________ (1 point)

2.For R₇ = {7, 8, 9, 10, 11, 12, 13, 14, 15}, what is the probability of a Type II error if the subject has a probability of p = 0.70 of identifying the odd sample on a single trial? ____________ (1 point)

3.For R₉ = {9, 10, 11, 12, 13, 14, 15}, what is the probability of a Type I error? ____________ (1 point)

4.For R₉ = {9, 10, 11, 12, 13, 14, 15}, what is the probability of a Type II error if the subject has a probability of p = 0.70 of identifying the odd sample on a single trial? ____________ (1 point)

(a)0.0152

(b)0.0223

(c)0.1484

(d)0.0308

(e)0.1311

(f)0.0085

(g)0.0500

(h)0.0173

(i)0.0882

(j)0.2030

Please solve using R. Thanks