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.