Construct a 4 * 4 addition table of binary 2-bit strings modulo 2. For example, 01 + 11 = 10 and 11 + 11 = 00. Replace each element in the table by its decimal equivalent plus 1. For example, 11 is replaced by 4. Is the resulting table a Latin square? Generalize this method for constructing Latin squares of order n

A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 450 students and finds that 214 are against the new legislation.

Calculate the EBP. Use a 90% Confidence Level. Fill in the blank, round to three decimal places.

BigBox Stores, Inc., has just purchased 100 acres of land in Happyville. The town, fearful of a huge chain store ruining the economy and putting local retailers out of business, quickly passes an ordinance restricting the size of any new buildings to no more than 5,000 square feet. The typical BigBox store averages approximately 100,000 square feet. Does the town of Happyville have the right to enact a zoning restriction of this nature?

Iron-deficiency anemia is an important nutritional health problem in the Unites States. A dietary assessment was performed on 51 boys 9-11 years old whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.5 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among 9-11 years old boys from all income strata is known to be 14.44 mg. Researchers are wondering if the mean iron intake among the low-income group is different from that of the general population.

a) Based on the sample of 51 boys provide a 95% confidence interval for the mean daily iron intake among boys 9-11 years old whose families were below poverty level. Interpret the interval.

b) Perform an appropriate two-sided test at α = 0.05 to answer the researcher’s question. Interpret the results.

c) Are the results in a) and b) consistent?

C++

Instructions

The population of town A is less than the population of town B. However, the population of town A is growing faster than the population of town B.

Write a program that prompts the user to enter:

1. The population of town A
2. The population of town B
3. The growth rate of town A
4. The growth rate of town B

The program outputs:

1. After how many years the population of town A will be greater than or equal to the population of town B
2. The populations of both the towns at that time.

(A sample input is: Population of town A = 5,000, growth rate of town A = 4%, population of town B = 8,000, and growth rate of town B = 2%.)

Two rural individuals Matyás and Toka are contemplating leaving their village for a nearby town. Given that Matyás has a secondary school certificate, she has a higher probability of obtaining an urban sector job than Toka, who is a primary school drop out. If they remain in the village and work on their family farms, they earn $200 each per year if the yield is high and $100 per year if the yield is low. The yield will be high with probability 0.5 and low with probability 0.5. Alternatively both these individuals can choose to migrate to town, in which case they each expect to find a formal or informal sector job, paying the following earnings according to the given probabilities.

1. (a) According to the Harris-Todaro model, on a one-year time horizon, which individual will migrate? [2 points]

2. (b) On the three-year time horizon, which individual(s) will migrate? (Assume the rate of interest at which both can borrow or lend money is i = 5%) [5 points]

3. (c) Assume a one-year time horizon. Suppose now that there is a traditional family support payment of $40 that all urban migrants must pay yearly to their relatives back in the village. At the same time, each bears a ‘psychological cost’ associated with moving to the city. Such a cost is $25 for Matyás and $15 for Toka. Again, according to the Harris-Todaro model, which farmer will migrate to town? [5 points]

4. (d) Assume a one-year time horizon, Still maintaining the ‘psychological’ costs associated with moving to the city, suppose now that all formal jobs also come with medical benefits, which are worth $30 a year, in additional to the wage. Informal sector jobs do not carry any such benefits. According to the Harris- Todaro model once again, which individuals will migrate to town? [3 points]

Let S be the educational attainment of individuals in a town, with values S=0 for less than high school and S=1 for high school or above. Also, let Y be their individual annual income with values Y=0 for less than $20,000, Y=1 for between $20,000 and $40,000, and Y=2 for above $40,000. Consider now the following joint probabilities:

A) Determine the expected value (mean) of the conditional expected level of educational attainment (given the various levels of individual annual income).

B) Determine the expected level of educational attainment.

The concession stand at the Shelby High School stadium sells slices of pizza during soccer games. Concession stand sales are a primary source of revenue for high school athletic programs, so the athletic director wants to sell as much food as possible. However, any pizza not sold is given away to the players, coaches, and referees, or it is thrown away. The athletic director wants to determine a reorder point that will meet, not exceed, the demand for pizza. Pizza sales are normally distributed, with a mean of 6 pizzas per hour and a standard deviation of 2.5 pizzas. The pizzas are ordered from Pizza Town restaurant, and the mean delivery time is 30 minutes, with a standard deviation of 8 minutes.

1. Currently, the concession stand places an order when it has 1 pizza left. What level of service does this result in?
2. What should the reorder point be to have a 98% service level?

Assume that newborn girls have birth weights with a mean of 3021 grams and a standard deviation of 694 grams. A random sample of 100 newborn girls is obtained and they have a mean birth weight of 2963 grams. What is the probability of randomly selecting another 100 newborn girls and getting a mean birth weight that is 2963 grams or​ lower?

Researchers aim to study the weights of 10-year-old girls living in the United States (possibly to compare to other countries and thus compare growth rates). Based on previous studies, we can assume that weights of 10-year-old girls are Normal. From a small sample of 16 girls, the researchers find a sample average of ?̅ = 91.4 pounds and a sample standard deviation of ? = 2.8 pounds. Create a 99% confidence interval for the true average weight of 10-year-old girls in the U.S. (and make a formal conclusion based on your calculated interval).