Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion about the null hypothesis, and final conclusion that addresses the original claim (Don’t just say Reject the null hypothesis or fail to reject the null hypothesis).

5. A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 147 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 16.7 lb.

146 140 160 151 134 189 157 144 175 127 164

Case Study Forecasting Attendance at SWU Football Games

Southwestern University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the Dallas/Fort Worth metroplex, enrolls close to 20,000 students. In a typical town–gown relationship, the school is a dominant force in the small city, with more students during fall and spring than permanent residents.

A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top 20 in college football rankings. To bolster its chances of reaching the elusive and long-desired number-one ranking, in 2008 SWU hired the legendary Billy Bob Taylor as its head coach. Although the number-one ranking remained out of reach, attendance at the five Saturday home games each year increased. Prior to Taylor’s arrival, attendance generally averaged 25,000 to 29,000 per game. Season ticket sales bumped up by 10,000 just with the announcement of the new coach’s arrival. Stephenville and SWU were ready to move to the big time!

The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in 1953, has seating for 54,000 fans. The following table indicates attendance at each game for the past 6 years.

One of Taylor’s demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head-on. Taylor had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.

SWU’s president, Dr. Marty Starr, decided it was time for his vice president of development to forecast when the existing stadium would “max out.” He also sought a revenue projection, assuming an average ticket price of $20 in 2014 and a 5% increase each year in future prices.

Discussion Questions

1. Develop a forecasting model, justify its selection over other techniques, and project attendance through 2015.

2. What revenues are to be expected in 2014 and 2015?

3. Discuss the school’s options.

Southwestern University Football Game Attendance, 2008–2013

2008 2009 2010 GAME ATTENDEES OPPONENT ATTENDEES OPPONENT ATTENDEES OPPONENT aHomecoming games. bDuring the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance. Source: J. Heizer and B. Render, Operations Management, 11th ed., © 2014. Reprinted and electronically reprod

In the late 1990s, the euro depreciated 15 percent against the dollar. As a result, European:

A. exports rose, boosting the economy. B. imports rose, boosting the economy. C. exports declined, dragging down the economy. D. imports declined, dragging down the economy.

Why did so many countries in Sub-Saharan Africa experience economic stagnation in the 1980s and 1990s? Is there any evidence of recovery in the last decade? Illustrate your answer with reference to literature and data relating to one or more Sub-Saharan African economy.

The accompanying data table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Complete the questions below. LOADING... Click the icon to view the data table. Use the range rule of thumb to identify a range of values containing the usual numbers of girls in 10 births. The maximum usual value is 0.2. ​(Round to one decimal place as​ needed.)x P(x)

0 0.004

1 0.017

2 0.043

3 0.112

4 0.206

5 0.234

6 0.202

7 0.114

8 0.041

9 0.011

10 0.016

A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 78 girls in 169 ​births, so the sample statistic of six thirteenths results in a z score that is 1 standard deviation below 0. -What is the null hypothesis and alternative hypothesis -what is the value of alpha -what is the sampling distribution of the sample statistic? -Is the test two-tailed, left tailed or right tailed? -what is the value of the test statistic? -P-value? -What are the critical values? - What is the area of the critical region? How to solve this with TI-83?

Consider an experiment in which a random family is selected among all families with exactly two children of which one is known to be a girl.

a. Write out the sample space and state the probability that the selected family has two girls.

b. Now consider an experiment in which we select a family randomly among all families with exactly two children, of which one is known to be a girl born on Tuesday. Write out the entire sample space taking into account the gender of the children and the day of the week they were born on.

c. What is the probability that the selected family has two girls?

d. Are the variables “day of the week” and “gender of child” dependent or independent?

In answering the question(s), make sure to write down the following 7 steps.

Step 1: Establish null and alternate hypotheses State the null and alternative hypothesis (as a sentence and formula).

Step 2: Calculate the degrees of freedom

Step 3: Calculate t _critical using critical t – table

Step 4: Calculate the Sum of Square deviation (SS_D)

Step 5: Calculate t _obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve

Step 7: Decision and Conclusion Write a clear and concise conclusion.

A researcher is interested in whether gender predicts the type of costume people would wear to an upcoming party. He asks 6 guys and 6 girls: How likely would you be to wear a “Creepy Clown” costume to the upcoming Halloween party? (1 = very unlikely to 7 = very likely). The data are shown below.

Guys: 4 6 4 3 6 7

Girls: 2 5 4 1 2 3

1. Use alpha = .01 to see whether gender impacts willingness to wear a Creepy Clown costume. (Note: You need to write down all the 7 steps.)

2. Use alpha = .01 to see whether guys are more willing than girls to a Creepy Clown costume. (Note: You only need to write down the steps that are different from part (1).)

3. Use alpha = .05 to see whether guys are more willing than girls to a Creepy Clown costume. (Note: You only need to write down the steps that are different from part (1).)

Denition:
An orthogonal array OA(k, n) on n symbols is an n² x k array such that, in any two columns, each ordered pair of symbols occurs exactly once.
Prove that there exists an OA(k, n) if and only if there exist (k - 2) mutually orthogonal Latin squares of order n.

(combinatorics and design)