The mean weekly unemployment benefit in the US was in 2003. A researcher in Virginia had a theory that the mean weekly unemployment benefit in Virginia was less than the national average. She took a random sample of 35 unemployment recipients in Virginia and found that the sample mean weekly unemployment benefit vow $231 with a sample standard deviation of $80. Use this information to answer questions 1 to 3.

1. State the appropriate hypotheses for this research hypothesis.

a. H₀: µ > $238  H_A: µ ≤ $23S

b. H₀: µ ≥ $238  H_A: µ < $238

c. H₀: µ ≤ $238  H_A: µ > $238

d. H₀: µ = $238  H_A: µ ≠ $238

e. H₀: µ ≠ $238  H_A: µ = $238

f. H₀: µ < $238  H_A: µ ≠ $238

2. Calculate a range for the p-value.

a. p-value < .01

b. .01 < p-value < .02

c. .02 < p-value < .05

d. .05 < p-value < .10

e. .10 < p-value < .20

f. p-value > .20

3. What is the researcher's conclusion?

a. Reject H₀.

b. Accept H₀.

c. Fail to reject H₀.

d. Fail to reject H_A.

e. Reject H_A.

f. Accept H_A.

The population proportion of US workers who belonged to unions in 2005 was 12.5%. Union officials want to know if their efforts to organize in 2006 increased union membership significantly. They took a sample of 400 US workers in 2006 and found that 52 belonged to unions. Use this information to answer questions 4 and 5.

4. What is the appropriate hypothesis test to determine whether union membership increased in 2006?

a. H₀: µ > .125  H_A: µ ≤ .125

b. H₀: µ ≤ .125  H_A: µ p > .125

c. H₀: µ = .125  H_A: 11 µ ≠ .125

d. H₀: p ≥ .125 H_A:  p < .125

e. H₀: p ≤ .125  H_A:  p > .125

f. H₀: p = .125  H_A: p ≠ .125

5. Calculate the p-value and state your conclusion using α = .05.