A random sample of 85 group leaders, supervisors, and similar personnel revealed that on the average a person spent 6.5 years on the job before being promoted. The standard deviation of the sample was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval within which the population mean lies?
Answer(s): E
Interval estimate can be found from x_bar +/-z*s/(n^0.5). Here we have n = 85, x_bar = 6.5 and z = 1.96 (for 95%) and s = 1.7. Therefore 6.5+/-1.96*1.7/9.22 and we get 6.14 and 6.86.
You are examining a group of 20 mutual funds. You find that 10 have a 5% cash position, 4 have a 10% cash position, and 6 have a 2% cash position. What is the weighted average cash position of these 20 mutual funds?
Answer(s): B
A weighted-average is equal to the sum (as i goes from 1 to n) of w_i * X_i, where w_i is the percentage weight of the ith item, and X_i is the value of the ith item. Here, we get a weighted mean of 10/20 * 0.05 + 4/20 * 0.10 + 6/20 * 0.02 = 5.10%.
What is the critical z-value for a one tailed lower test at the 1% level of risk?
This is found by subtracting the 0.01 from 0.5 and then finding the z-value for 0.49.
What is the annual Internal Rate of Return of this series of annual cash flows: Year 0: <$15,000>, Year 1:$2,000, Year 2: $0, Year 3: $15,000, Year 4 to indicate a negative number).
On the BAII Plus, press CF 2nd CLRWork 15000 +/- ENTER DownArrow 2000 ENTER DownArrow DownArrow 0 ENTER DownArrow DownArrow 15000 ENTER DownArrow DownArrow 0 ENTER DownArrow DownArrow 18000 ENTER DownArrow DownArrow 2nd Quit. Then press Irr CPT. On the HP12C, press these keys: 15000 CHS BlueShift CFo 2000 BlueShift CFj 0 BlueShift CFj 15000BlueShift CFj 0 BlueShift CFj 18000 BlueShift CFj. Then press YellowShift Irr. The "DownArrow" represents the downward-pointing arrow on the top row of the BAII Plus keyboard. Make sure the BAII Plus has the P/Y value set to 1.
Suppose you are modeling GNP, and you believe that the probability that GNP will expand if interest rates fall is 70%; if interest rates stay constant, you believe that there is a 29% chance of expanding GNP; if interest rates increase, you believe that there is a 1% chance of GNP expanding. You think that the likelihood of interest rates falling is 60%; of staying the same is 30%; of increasing is 10%. What is the unconditional probability of GNP expanding?
Answer(s): C
We use the total probability rule: P(A), the unconditional probability, = P(A|S_1)*P(S_1) + P(A|S_2) *P(S_3) + P (A|S_3) *P(S_3), where the S_i represent mutually exclusive and exhaustive events. So the likelihood of interest rates increasing is 0.70 * 0.60 + 0.29 * 0.30 + 0.01 * 0.10 = 0.42 + 0.087 + 0.001 = 0.508.
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