Question

1. The value of z_α/2 when determine the 96% confidence interval for p.

2. The decision rule (aka, the rejection region) for testing the following pair of hypotheses at the .05 level of significance when the population standard deviation is unknown and a random sample of size 28 is taken.

H₀: µ = 18

H_a: µ < 18

3. The value of t_α/2 when determine the 99% confidence interval for µ when the sample standard deviation of the population is unknown and a sample size of 35 was taken from a normally distribution random variable

4. P(Y > 57) where Y has a normal distribution with µ = 64 and σ = 7.

Provide diagrams as well

Answer 1

a) At α = 0.04 two tailed critical value, z_α/2 = ABS(NORM.S.INV(0.04/2)) = +/- 2.054

b)

df = n-1 = 27

Critical value, t-crit = T.INV(0.05, 27) = -1.703

c)

At α = 0.01 and df = n-1 = 34, two tailed critical value, t_α/2 = T.INV.2T(0.01, 34) = +/- 2.728

d)

µ = 64, σ = 7

P(X > 57) =

= P( (X-µ)/σ > (57-64)/7)

= P(z > -1)

= 1 - P(z < -1)

Using excel function:

= 1 - NORM.S.DIST(-1, 1)

= 0.8413