Question

1. The decision rule (aka, the rejection region) for testing the following pair of hypotheses at the .01 level of significance when a sample size of 45 is taken.

H₀: p = .45

H_a: p ≠ .45

2. P (p̂ < 0.35) where p̂ is approximately normally distributed with p = .33 and n = 100.

c. Determine the p-value for testing:

H₀: µ = 43

H_a: µ ≠ 43

when a random sample of size 30 was taken from a normal population whose standard deviation is known and the value of the test statistic equals -1.38.

4. P (ŷ> 22) where Y has a normal distribution with a mean of 20, a standard deviation of 8, and, when a sample size of 25 was taken.

Answer 1

a)

b)

c)

p value = 2*P(Z<-1.38) = 0.168

d)

P(Y > 22) = P(Y - mean > 22 - mean)
                  = P( (Y - mean)/(SD/root(N)) > (22 - mean)/(SD/root(N))
                  = P(Z > (22 - mean)/(SD/root(N)))
                  = P(Z > (22 - 20)/1.6)
                  = P(Z > 1.25)
                  = 1 - P(Z <= 1.25)
                  = 0.106