Consider:

(a) Stock trades for $100;

(b) Calls with exercise prices of $90, $100, and $110 trade at prices of $17.11, $10.69, and $6.10 respectively.

If a person buys a $90 call, writes two $100 calls, and buys a $110 call, what is her higher break-even point? The answer is 108.17, how do you solve this?

A 200 mL solution of .100 M solution of Ammonia, NH3, is slowly mixed with .100 M HCl. Determine the pH after addition of: 0 ml of HCl, 50 mL of HCl, 100 mL of HCl, 200 mL of HCl, and 250 mL of HCl.

Consider a sample of 100 helium atoms (He) and a sample of 100 argon atoms (Ar). Which sample weighs more? The helium or argon sample? Briefly explain your reasoning

A 200 mL solution of .100 M solution of Ammonia, NH3, is slowly mixed with .100 M HCl. Determine the pH after addition of: 0 ml of HCl, 50 mL of HCl, 100 mL of HCl, 200 mL of HCl, and 250 mL of HCl.

A person bets 100 times on events of probability 1/100, then 200 times on events of probability 1/200, then 300 times on events of probability 1/300, then 400 times on events of probability 1/400 If the events are assumed to be independent what is the appromate distribution of the number of times the person wins?

1. Everyone likes to be 100% certain with results. Why can't you be 100% certain with confidence intervals?

2. Discuss the pros and the cons of using a higher level of confidence. For example if you can't be 100% certain, what would be the benefit and the disadvantage of using 99% or even 99.9%?  

3. How should you decide what level to use? Are there times when one level might be more appropriate than the other?

Given the following hypothesis:

H0: μ = 100 H1: μ ≠ 100

A random sample of six resulted in the following values:

118 ,120 ,107 ,115 ,115 ,107

Using the 0.02 significance level, can we conclude that the mean is different from 100?

a. What is the decision rule? (Negative answer should be indicated by a minus sign. Round the final answers to 3 decimal places.)

Reject H0: μ = 100 and accept H1: μ ≠ 100 when the test statistic is ( , ).

b. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

Value of the test statistic c. What is your decision regarding H0? H0 .

d. Estimate the p-value.

e-1. Construct a 98% confidence interval. Confidence interval is from to .

e-2. Use the results of the confidence interval to support your decision in part (c). H0 .

An urn contains 100 balls that have the numbers 1 to 100 painted on them (every ball has a distinct number). You keep sampling balls uniformly at random (i.e., every ball is equally likely to be picked), one at a time, and without replacement. For 1 ? i < j ? 100, let E_{i,j} denote the event that the ball with the number j was taken out of the urn before the ball with the number i. Prove that the events E_{45,89} and E_{23,60} are independent. Are E_{13,72} and E_{72,99} also independent? Why or why not?

Hint: You might want to think of the outcomes as permutations of 1 to 100, and ? as the set of all possible permutations of 1 to 100 (why?).

In a recent survey of county high school students, 100 males and 100 females, 66 of the male students and 47 of the female students sampled admitted that they consumed alcohol on a regular basis. Find a 90% confidence interval for the difference between the proportion of male and female students that consume alcohol on a regular basis. Can you draw any conclusions from the confidence interval?

For the test of significance questions, clearly indicate each of the formal steps in the test of significance.

Step 1: State the null and alternative hypothesis.
Step 2: Calculate the test statistic.
Step 3: Find the p-value.
Step 4: State your conclusion. (Do not just say “Reject H0” or “Do not reject H0”, state the conclusion in the context of the problem.)

Country A has 100 machines (physical capital) and a population of 100 (out which 80 are in the labour force). Discuss the effect on real GDP per capita if a. Population doubles (keeping machines constant at 100) b. Machines double (keeping the population constant at 100)