In a famous research paper in the psychology literature, George Miller found that the amount of information humans could process in short-term memory was 7 bits (pieces of information), plus or minus 2 bits. Let us assume that the title of Miller’s paper ("The Magical Number Seven, Plus or Minus Two") refers to a 95% confidence interval for the population mean amount of information processed by humans in bits, is found to be between 5 bits to 9 bits.

1. What is the sample mean for the amount of information processed by humans?

2. A fixed level of significance of 5% was selected to test the hypotheses H0: μ = 6.1 bits versus Ha: μ ≠ 6.1 bits. What would be your statistical decision?

a. Fail to reject H0

b. Reject H0

c. Cannot tell

3. A fixed level of significance of 10% was selected to test the hypotheses H0: μ = 10 bits versus Ha: μ ≠ 10 bits.. What would be your statistical decision?

a. Fail to reject H0

b. Reject H0

c. Cannot tell

4. A fixed level of significance of 10% was selected to test the hypotheses H0: μ = 5.5 bits versus Ha: μ ≠ 5.5 bits. What would be your statistical decision?

a. Fail to reject

b. Reject

c. Cannot tell