Given the following information, what is the percentage dividend yield between today and period 1? Today’s Dividend = $3.69 Expected Growth rate in dividends = 3.14 Discount Rate (Required return) = 8.53 Calculate your answer to two decimal places (e.g., 2.51)

Directions: All calculations involving interest rates should be answered as a percentage to two decimal places, for example 5.42% rather than 0.05.

1.) A bank has $50M in rate-sensitive assets and $35M in rate-sensitive liabilities. What is the impact on the bank’s profits if rates decrease by 50 basis points?

Here are the percentage returns on two stocks.

a-1. Calculate the monthly variance and standard deviation of each stock. (Do not round intermediate calculations. Round your answers to 1 decimal places.)

b. Now calculate the variance and standard deviation of the returns on a portfolio that invests an equal amount each month in the two stocks. (Do not round intermediate calculations. Round your answers to 1 decimal places.)

c. Is the variance more or less than half way between the variance of the two individual stocks?

Ask the user to enter a basketball player’s free throw percentage, eg. 70%. Your program will simulate the player playing 5 games, each game making 10 free throws. Display the result of the free throws in each game. At the end, print a summary that shows the best/worst game for this player, and the average free throw percentage of the 5 games. Question: How do you simulate a 70% free throw shooter making a free throw? Hint: How about generating a number between 0-100, and checking if that number is less than or equal to 70. If so, you just made a free throw!

STAT 200 Week 1 Homework Problems

1.1.4 To estimate the percentage of households in Connecticut which use fuel oil as a heating source, a researcher collects information from 1000 Connecticut households about what fuel is their heating source. State the individual, variable, population, sample, parameter, and statistic

1.1.8 The World Health Organization wishes to estimate the mean density of people per square kilometer, they collect data on 56 countries. State the individual, variable, population, sample, parameter, and statistic

1.2.4 You wish to determine the GPA of students at your school. Describe what process you would go through to collect a sample if you use a stratified sample.

1.3.4 To evaluate whether a new fertilizer improves plant growth more than the old fertilizer, the fertilizer developer gives some plants the new fertilizer and others the old fertilizer. Is this an observation or an experiment? Why?

1.3.10 A mathematics instructor wants to see if a computer homework system improves the scores of the students in the class. The instructor teaches two different sections of the same course. One section utilizes the computer homework system and the other section completes homework with paper and pencil. Are the two samples matched pairs or not? Why or why not?

1.3.16 To determine if a new medication reduces headache pain, some patients are given the new medication and others are given a placebo. Neither the researchers nor the patients know who is taking the real medication and who is taking the placebo. Is this a blind experiment, double blind experiment, or neither? Why?

1.4.2 Suppose a car dealership offers a low interest rate and a longer payoff period to customers or a high interest rate and a shorter payoff period to customers, and most customers choose the low interest rate and longer payoff period, does that mean that most customers want a lower interest rate? Explain.

1.4.8 Suppose a telephone poll is conducted by contacting U.S. citizens via landlines about their view of same sex marriage. Suppose over 50% of those called do not support same sex marriage. Does that mean that you can say over 50% of all people in the U.S. do not support same sex marriage? Explain

1.4.14 An employee survey says, “Employees at this institution are very satisfied with working here. Please rate your satisfaction with the institution.” Discuss how this question could create bias.

2.1.4 In Connecticut households use gas, fuel oil, or electricity as a heating source. Table #2.1.7 shows the percentage of households that use one of these as their principle heating sources ("Electricity usage," 2013), ("Fuel oil usage," 2013), ("Gas usage," 2013). Create a bar chart and pie chart of this data. State any findings you see from the graphs.

Table #2.1.7: Data of Household Heating Sources

Assuming atoms of radius of 1.00 Å and atoms just touching one another, calculate the percentage of the volume taken up in a face-centered cubic unit cell by those atoms.

Graph the year-over-year percentage growth of home prices in XX and explain the economic impact.

The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers. Soil water content from field I: x1; n1 = 72 15.1 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.9 11.2 Soil water content from field II: x2; n2 = 80 12.2 10.2 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.5 14.0 14.5 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) (b) Let ?1 be the population mean for x1 and let ?2 be the population mean for x2. Find a 95% confidence interval for ?1 ? ?2. (Round your answers to two decimal places.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? All negative? Of different signs? At the 95% level of confidence, is the population mean soil water content of the first field higher than that of the second field? Because the interval contains only positive numbers, we can say that the mean soil water content of the first field is higher. Because the interval contains both positive and negative numbers, we cannot say that the mean soil water content of the first field is higher. We can not make any conclusions using this confidence interval. Because the interval contains only negative numbers, we can say that the mean soil water content of the second field is higher. (d) Which distribution did you use (standard normal or Student's t)? Why? The Student's t-distribution was used because ?1 and ?2 are known. The standard normal distribution was used because ?1 and ?2 are unknown. The Student's t-distribution was used because ?1 and ?2 are unknown. The standard normal distribution was used because ?1 and ?2 are known. Do you need information about the soil water content distributions? Both samples are small, so information about the distributions is not needed. Both samples are small, so information about the distributions is needed. Both samples are large, so information about the distributions is not needed. Both samples are large, so information about the distributions is needed. (e) Use ? = 0.01 to test the claim that the population mean soil water content of the first field is higher than that of the second. (i) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2 H0: ?1 = ?2; H1: ?1 ? ?2 H0: ?1 ? ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 (ii) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference ?1 ? ?2. Do not use rounded values. Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.

The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data.

(a) Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. Use a 0.05 level of significance.

State the null and alternative hypotheses:

A. H₀: Not all proportions are equal.
H_a: p_Sun ≠ p_Mon ≠ p_Tue ≠ p_Wed ≠ p_Thu ≠ p_Fri ≠ p_Sat ≠

B. H₀: Not all proportions are equal.
H_a: p_Sun = p_Mon = p_Tue = p_Wed = p_Thu = p_Fri = p_Sat =

C. H₀: p_Sun ≠ p_Mon ≠ p_Tue ≠ p_Wed ≠ p_Thu ≠ p_Fri ≠ p_Sat ≠

H_a: All proportions are equal.

D. H₀: p_Sun = p_Mon = p_Tue = p_Wed = p_Thu = p_Fri = p_Sat =

H_a: Not all proportions are equal.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

State your conclusion:

A. Reject H₀. We conclude that the proportion of traffic accidents is not the same for each day of the week.

B. Do not reject H₀. We conclude that the proportion of traffic accidents is the same for each day of the week.     

C. Do not reject H₀. We conclude that the proportion of traffic accidents is not the same for each day of the week.

D. Reject H₀. We conclude that the proportion of traffic accidents is the same for each day of the week.

(b) Compute the percentage of traffic accidents occurring on each day of the week. (Round your answers to two decimal places.)

Sunday _____%

Monday _____%

Tuesday _____%

Wednesday _____%

Thursday _____%

Friday _____%

Saturday _____%

What day has the highest percentage of traffic accidents?