### T-statistics vs. z-statistics

Why is a t-statistic, as opposed to a z-statistic, used to test small populations? When does the t-statistic approximate the z-statistic?

Why is a t-statistic, as opposed to a z-statistic, used to test small populations? When does the t-statistic approximate the z-statistic?

The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's

A synopsis of a business related problem where statistics was used to solve the problem. The synopsis needs to include a discussion of the specific problem, the research methodology used, the quantitative and qualitative tools used, and the benefit and limitations of the resolutions used.

A recent article in the Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 At the .01 significance level, can we conclude that the 30-year mortgage rate for sm

(See attached files for full problem description) --- 1. Case Analysis: Riverside Chamber of Commerce Introduction All case studies address the following points: a. Define the problem statement b. Define any and all assumptions made to address the case study c. Analyze the data utilizing concepts and knowledge relevant

1 The U.S. Fish and Wildlife Service's report on the bass population in the North American lakes indicated average weight of the fish to be 3.0 lb. and a standard deviation of .30 lb. Furthermore, 50% of all bass were females. The State of Florida conducted an independent study and reported the average weight of their bass wa

A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and

Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant

(See attached files for full problem description)

Give an example of a hypothesis test you could perform at a Surgery Center and what the hypotheses would be. State the null and alternative hypotheses in proper format. Would you see this as a one time test or one that would be repeated on a regular basis?

Presume that the statistics say that the chances of surviving after brain surgery is 25%. So the Surgery Center would like to test whether it is 25% or less. Conduct a hypothesis test.

The following data are the heart rates (in beats per minute) of 12 regular before and after chewing smokeless tobacco. Does chewing make a difference in heart rate? Also, is the test dependent or independent? Subject 1 2 3 4 5 6 7 8 9 10 11 12 Rate Before

A common method of checking for pollution in a river is to measure the dissolved oxygen content in the river water at different locations. A reduction of oxygen content in the water from one location to another indicates the presence of pollution somewhere between the two locations. The Environmental Protection Agency (EPA) su

To learn about the effect of a newly developed gasoline additive on gas mileage (mpg), seven cars were driven 300 miles first without additive and then 300 miles with a gas additive. Here are the mpg's. Did the new additive improve gas mileage? Also, is the test dependent or independent. Car # m

To increase rainfall, extensive cloud-seeding experiments are to be conducted, and the results are to be compared with a baseline figure of .54 inch of rainfall ( for comparable periods when cloud seeding wasn't done). Set up the hypothesis only and decide if you have a 2 tail, 1 tail upper, or 1 tail lower test.

A real estate developer is considering investing in a shopping mall on the outskirts of Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the income in the area surrounding the proposed mall. A random sample of four families is selected near each proposed mall. Following are the sample resu

Give an example of a hypothesis test you could perform at a Surgery Center and what the hypotheses would be. State the null and alternative hypotheses in proper format. Would you see this as a one time test or one that would be repeated on a regular basis?

The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours s

A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and

The Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations

The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using

The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05 signi

7. There is a program for STD/HIV/pregnancy education/prevention called Postponing Sexual Involvement (PSI) run in Atlanta. Evaluation data collected at the end of ninth grade as a follow-up to the program compared two group of adolescents - one treatment and one control - all of whom had not had sex at the pretest (beginning o

8. News flash from Science News (June 2, 2001). Researchers reported that breast feeding children seemed to accelerate the progression of AIDS. A study done in 1993(?!) randomly assigned HIV positive volunteer women to either a breast-feeding or bottle feeding group. Of the 200 women who used commercial formula, 6 died during th

1. The Dean is hanging his head in shame. He realizes his failings in designing an adequate research design to assess the effects of the move on majors and has revised the proposal. Unfortunately, the word processor used (WordImperfect) has scrambled the text and he needs help in correcting the text. In the paragraphs below, h

Chicken Delight claims that 90% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 100 orders revealed that 82 were delivered within the promised time. At the 0.10 significance level, can we conclude that less than 90% of the orders are delivered in less than 10 minutes? Please sho

The following hypothesis are given. H0: σ2/1 ≤ σ2/2 H1: σ2/1 > σ2/2 A random sample of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. At the .01 significance level

(See attached file for full problem description) --- 1. On a college bulletin, it is stated that the weights of the male students are normally distributed with mean = 165lb and a standard deviation = 16lb. A research student decided to verify the claim of the school by taking a sample of 64 students. The average weight of the

10. A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte's Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Compute z values for each and

Of all the presidents since WWII, Jimmy Carter suffered the worst overall approval rating at 45%. George W. Bush's approval rating varied widely. It reached a high of 90% just after 9/11, but in mid-July, it stood at 49% as measured by CNN/USA Today/Gallup poll of 1000 randomly selected adults. Is there evidence to suggest that