Stats Professor Exam 1

Directions: Try to take the exam as if it were an actual test.  When you finish, click the problems one-by-one to check your answers.  There is a view answer link to just see the text solution, but if you got the problem wrong, you should watch the included video as well. 

1. Determine whether the given value is a statistic or a parameter:

i)  A sample of 1,000 Americans revealed that only 1 in 6 (16.7%) of them have blue eyes.

ii) The average age of the set of current US senators is 61.7 years old.

2. A group of researchers would like to know the average body fat percentage for fifth grade girls in the United States.  To estimate this, they use a stratified sampling approach to randomly sample 1,500 fifth graders from across the country.  Identify the population of interest to the researchers.

3. Find the class boundaries for the following frequency distribution:

4. Determine whether the given value is from a discrete or continuous data set:

i. A randomly selected freshman backpack weighs 37.8 pounds.

ii. On a randomly selected day in May, an AMEX call center receives 8,153 calls.

5. A study finds the average amount of money spent at Macy's per purchase is $123.51, what units would the variance have?

6. Laptop weights are normally distributed with an average weight of 6 pounds and a standard deviation of 0.78 pounds.  What percentage of laptops weigh between 5.22 and 6.78 pounds?

7.   The average American (over 15yrs old) watches 2.8 hours of TV per day with a standard deviation of 1.3 hours.  What can you conclude from Chebyshev's theorem about the percentage of Americans who watch between 0.1 and 5.5 hrs of TV per day?

8.  Find the relative frequency distribution from the following frequency distribution:

9.  The average weight of male adults is 172 lbs with a standard deviation of 29 lbs. Assuming nothing is known about the distribution of male weights, what percentage of males will weigh more than 240 lbs?

10. Calculate the variance of a sample for which:  ∑X =1,368.13 ; ∑X² = 48,572.47 ; and n =39.

11. In the drawing below, label the mean, median, and mode:

12. I use an excel spread sheet to record all of my students’ grades.  The spread sheet calculates and reports the mean and median for each exam.  While reviewing the scores for exam two, I notice that the mean is 71.8 and the median is 74.2.  What type of distribution most likely describes the shape of the test scores: skewed left, skewed right, or symmetric?

13. A data set contains the observations: 2, 4, 7, 3, 1, -1, 8, and 9.  Calculate:

14. A list of home values (in thousands) is given.  The list was obtained from a random selection of condos in Deerfield Beach, FL:  $35, $128, $55, $45, $75, $62, $423.  If you wanted to use this data to find a measure of the center to describe the typical cost of a condo in Deerfield Beach, what measure would be best to choose (mean, median, or mode)?

15. Find the class width used to create the following frequency distribution:

16. Men have average hip widths of 14.4 inches and a standard deviation of 0.9 inches.  If a man has a hip width of 16.1 inches, how many standard deviations away from the mean is his hip width? 

17.  Which do you think has more variation:  the ages of 40 people drinking in a bar on South Beach on a typical Friday night, the ages of 40 people walking around the Aventura shopping mall, or the ages of 40 randomly selected eighth graders from Dade county middle schools?

18. Women have an average buttock-to-knee length of 22.7 inches and a standard deviation of 1.0 inches.  Is it unusual for a woman to have a buttock-to-knee length of 26.6 inches long?

19. Which is better a score of a 90 on an exam with an average of 78 and a standard deviation of 12 or a score of a 78 on an exam with a mean of 70.5 and a standard deviation of 7.1?        

20.  After analyzing several large samples from the population of Quality Cola “12 oz” cans, company researchers have concluded that the distribution of actual soda can volumes is mound shaped and symmetric.  The cans appear to have an average volume of 11.8 ounces and a standard deviation of 0.72 ounces.  Give an interval of volumes that will contain approximately 95% of the population of Quality Cola cans. 

21. The Census Bureau’s short form for the 2000 census asked participants to report the following pieces of information: Name, age, sex, race, and number of people living in the residence.  Classify each of the variables listed above as Qualitative or Quantitative. 

22. Calculate the standard deviation for the following sample of values: 4.1, 2.3, 7.0, 8.9, 6.7, and 7.1.