I’m going to go easy on you for this one! We learned a lot about the t-Test for independent samples, and last week you compared estimated speed (in miles) for smashed into group and hit group. This week, I want you to review that assignment and NOW compute the effect size (Cohen’s D using the pooled variance). To make sure you have all the data you need to calculate the effect size, here are the means and standard deviations for the "hit" and "smashed into" groups from last week.

Group #1: Smashed into mean and SD: Mean = 41.55, Variance = 44.15, SD = 6.64

Group #2: Hit mean and SD:   M = 27.6, Variance = 53.94, SD = 7.34

1. Compute the effect size (Cohen’s d using the pooled variance). Which of the following is the effect size? Round 2 decimal points.
2. What does the pooled Cohen’s d you obtained using the coin study data represent?

3. What is the effect size and why do we report it?

A) Hypothesis Testing - Type I and Type II errors: You test the claim that the mean gas mileage of all cars of a certain make is less than 29 miles per gallon (mpg). You perform this test at the 0.10 significance level. What is the probability of a Type I error for this test?

B)Sleep: Assume the general population gets an average of 7 hours of sleep per night. You randomly select 40 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.69 hours with a standard deviation of 0.40 hours. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.01 significance level.
What is the test statistic? Round your answer to 2 decimal places. t_x=

What is the critical value of t? Use the answer found in the t-table or round to 3 decimal places.
t_α =

1. A nonprofit consumer-protection organization compares three types of front bumpers for automobiles.   The organization wishes to see whether the type of bumper makes a difference in protecting cars from damage. Tests are conducted by driving an automobile into a concrete wall at 15 miles per hour. The outcome examined is the amount of damage to the car, as measured by repair costs in hundreds of dollars. Due to the large costs of this type of testing, the organization only conducts two tests with each bumper type. The following table shows the results. The organization decides to analyze the data by conducting an analysis of variance.

1. Write out the null and alternative hypotheses.
2. Find the within-groups sum of squares, its degrees of freedom, and the associated mean square.
3. Find the between-groups sum of squares, its degrees of freedom, and the associated mean square.
4. Calculate the test statistic and determine its p-value. Can you reject the null hypothesis at the 0.05 level? At the 0.01 level?

True and False

15 The index of refraction is about 7.8 for glass.

16. Energy is always conserved.

17. A car traveling 40 miles in ½ hour is traveling at 20 mph.

18. 40 ^o C is hotter than 40^o F .

19. Objects with a density less than 1000 kg/m³ float.

20. Like charges repel and unlike charges attract

21. Electric current is more dangerous than voltage.

22.   Protons and electrons are found in the nucleus of atoms.

23 The atomic number of an element is the number of protons.

24. Electrons surround the nucleus of an atom and each has its own energy state.

25. An object that approaches you makes a sound having a higher pitch or frequency than normal.

26. The Doppler effect is a change in frequency due to the relative motion of a source of sound

29. A magnifiing glass when used to enlarge letters on a page is producing a virtual image.

Propagation Delay

A satellite phone connects to orbiting satellites instead of terrestrial cell sites. When you speak into a satellite phone , the signal has to travel from you to the satellite, from the satellite to the other person, and all the way back from the other person to the satellite and then satellite to you. What is the round trip propagation delay when you use a satellite phone for communication? You may assume that the satellite orbits at a height of 21,000 miles from the surface of the earth. This is the size of the orbit used by geosynchronous satellites whose orbital period is 24 hours, this means that the satellite is always over the same point on the planet. Because of this delay many satellite phone systems use groups of satellites with lower orbits and hand off the calls between them. Satellite TV systems do use geosynchronous satellites so that you can just point your dish at one point in the sky. Delay is less of a problem for one way communications such as video or other broadcasts. Careful: you need to convert to a consistent set of units to use in your calculation.

1. Jack, a geologist, opened a business organized as a C corporation called Geo-Jack (GJ) in January of this year. Jack is the sole shareholder. Assume GJ reports on a calendar year and uses the accrual method of accounting. For each item below, indicate its effect on Jack’s taxable income and you must clearly indicate whether it is positive or negative.
   1. In January, GJ rented a small business office about 12 miles from Jack’s home. GJ paid $14,000, which represented a damage deposit of $6,000 plus rent for two years ($4,000 annually).

______________

2. GJ earned and collected $300,000 performing geological-related services and selling its specialized digging tool.

______________

3. GJ purchased some new equipment in February for $53,700. It claimed depreciation on these assets during the year in the amount of $4,510.

______________

4. GJ paid Jack’s father $12,000 for services that would have cost no more than $7,000 if Jack had hired any other local business to perform the services. While Jack’s dad was competent, he does not command such a premium from his other clients.

Assignment No. 3.4

PROBLEM: Suppose you are the administrator in charge of setting the toll for crossing a toll bridge across a river. The current toll is $1 per trip and at that toll 1000 trips per hour are taken across the bridge. (a) If the price elasticity of demand for trips is 2.0, what will happen to the number of trips taken per hour if you raise the toll by 10 percent? How would this affect the total revenue collected per hour?(b) If the price elasticity of demand for trips is 0.5, what will happen to the number of trips taken per hour if you raise the toll by 10 percent? How would this affect the total revenue collected per hour?(c) Other things equal, at the current toll of $1, what do you think will happen to the elasticity of demand for trips, if the average incomes of people who use the bridge rise? Explain why.(d) Other things equal, at the current toll of $1, what do you think will happen to the elasticity of demand for trips if a non-toll bridge is built a few miles up the river? Explain why.

5) Background: You have developed a unique robotic device that will autonomously deliver groceries to people’s house. Facts: • You are limiting your delivery service to 3 miles from store location. • The cost to produce the delivery robot is $9,300 per robot with a 3 year lifecycle • Market research indicates you will need 5 robots to meet demand and account for down time (repair, charging, etc) • You expect to receive on average 75 orders per day • The average ticket price per order is $74 • It cost on average including maintenance and electricity 15 cents per mile to operate the delivery robot • Each order cost $8 in labor to pick the groceries and launch the robot • Margin for groceries is 3% Using break even analysis determine the minimum service fee per delivery you will have to charge for this service to insure you don’t lose money. Make sure you state your assumptions and show your work. I’m interested in your thought process. Feel free to submit as an excel spreadsheet if that’s easier.

1)

A) The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 45 and a standard deviation of 4. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 45 and 57?

B) A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 36 and 39 months?

C) The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 60 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 36 and 76?