# Hypothesis Testing, Confidence Interval & Probability

4. Using the data below, make a histogram, box plot, compute the mean, median, mode and standard deviation

City and State Crime

Albuquerque, NM 8515

Anaheim, CA 2827

Anchorage, AK 4370

Arlington, TX 5615

Atlanta, GA 10759

Aurora, CO 5079

Austin, TX 6406

Birmingham, AL 7030

Boston, MA 4986

Buffalo, NY 5791

Charlotte, NC 7484

Chicago, IL 6333

Cincinnati, OH 5694

Cleveland, OH 5528

Colorado Springs, CO 4665

Columbus, OH 8247

Corpus Christi, TX 6266

Dallas, TX 8201

Denver, CO 4685

Detroit, MI 8163

El Paso, TX 5106

Fort Worth, TX 6636

Fresno, CA 6145

Honolulu, HI 4671

Houston., TX 6084

Indianapolis, IN 4306

Jacksonville, FL 6118

Kansas City, MO 9882

Las Vegas, NV 4520

Lexington, KY 5315

Long Beach, CA 3407

Los Angeles, CA 3306

Louisville, KY 5102

Memphis, TN 6958

Mesa, AZ 5590

Miami, FL 8619

Milwaukee, WI 6886

Minneapolis, MN 7247

Nashville, TN 7276

New Orleans, LA 6404

New York, NY 2968

Newark, NJ 6068

Oakland, CA 6820

Oklahoma City, OK 8464

Omaha, NE 5809

Philadelphia, PA 5687

Phoenix, AZ 6888

Pittsburgh, PA 5246

Portland, OR 6897

Raleigh, NC 6327

Riverside, CA 3610

Sacramento, CA 5859

San Antonio, TX 6232

San Diego, CA 3405

San Francisco, CA 4859

San Jose, CA 2363

Santa Ana, CA 3008

Seattle, WA 8397

St. Louis, MO 11765

St. Paul, MN 6215

Stockton, CA 5638

Tampa, FL 8675

Toledo, OH 6721

Tucson, AZ 8079

Tulsa, OK 6234

Virginia Beach, VA 3438

Washington, DC 6434

Wichita, KS 5733

5. In child custody case, about 70% of the fathers win the case is they contest it. IN the next thee custody cases what is the probability that all three win

6. SOB's systolic blood pressure is a random variable with a mean of 145 mmHG and a standard deviation of 20mmHG. If the SOB's blood pressure is taken at a randomly chosen moment what is the probability it will be below 135? What is the probability it will be over 175?

7. Find the required sample size to estimate the mean starting salary for a new CEO with a 95% confidence, assuming the standard deviation is $7,500 with an error of $2,000. Assume the population N is 1,250,000.

8. 95% of Popcorn kernels take between 100 and 200 seconds to pop. What sample size (number of kernels) would be needed to estimate the true mean seconds to pop with and error of 5 seconds and 95% confidence level?

9. A sample of 20 pages was taken from the 2,000 page phone directory. On each page, the mean area devoted to display ads was shown - see data below. Construct a 95% confidence interval for the true mean

Display Ads

0

260

356

403

536

0

268

369

428

536

130

268

396

469

536

162

338

403

536

536

10. Stores are not supposed to sell cigarettes to teenagers. Of 320 stores checked, 82 stores sold cigarettes to teens. Is the goal being achieved is to reduce the % of stores selling cigarettes to under 20%. (1) Do a hypothesis test to reject or fail to reject the Ho and (2) construct a 95% confidence interval to determine the true percent of stores who allow teens to purchase cigarettes.

11. The mean number of arrivals at Chicago O'Hare is 195 flights per hour. The historical standard deviation of flight arrivals at O'Hare is 13. Using the data below, set up a hypothesis test to see if there has been an increase in arrivals. Would you arrive at a different decision if Alpha were .01?

Flights

210

215

200

189

200

213

202

181

197

199

193

209

215

192

179

196

225

199

196

210

199

188

174

176

202

195

195

208

222

221

12. One group of accounting students took an online course, The second groups of students took the same accounting course in a traditional classroom. At Alpha of .10 is there any difference in the results. Find p-value and interpret it

Online Students Classroom

Mean 9.1 10.3

Sample Std.dev. 2.4 2.5

N count 20 20

13. In a lottery each digit is supposed to have the same probability of occurrence. The table below shows the occurrence of each digit of 89 consecutive daily drawings. The Research questions is: at the .01 Alpha can you reject the Ho that the digits are from a uniform population.

Digit Frequency

0 39

1 27

2 35

3 39

4 35

5 35

6 27

7 42

8 36

9 41

Total 356

14. A sample of 100 mortgages approved during the course of a year showed that 31 were issued to single-earner family or individual. The historical average is 25%. Has the percentage of single-earned or individual mortgages risen? Test using Alpha .05.

See attached file.

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, sample size, confidence interval, normal probability and descriptive statistics. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.