1. Grades for ten students are: 88, 93, 83, 97, 73, 88, 85, 59, 73 and 79. Determine the following:
a. Measures of central tendency: mean, median, and mode
b. Measures of dispersion: range, top 20th percentile, and standard deviation
c. Should any scores be omitted in computing the above statistics, and if so, why?
2. Aggregate responses to three questions were obtained from a survey of 100 males and 100
females who were randomly selected and viewed three films (A, B and C) as shown below.
In the following table, indicate the type of scale (nominal, ordinal, interval, ratio), measure(s)
of central tendency (mean, median, mode) and dispersion (range, percentiles, standard
deviation) appropriate for each question. [Note: No calculations are required]
1. Film preference rankings (1 = 1st, 2 = 2nd, 3 = 3rd) for all respondents: A = 3, B = 2, C = 1
3. Satisfaction levels (Satisfied-Dissatisfied-No opinion: coded S-D-N) for each film:
A: S=29%, D=47%, N=24%; B: S=33%, D=29%, N=38%; C: S=68%, D=27%, N=5%
3. Violence ratings (1=Low, 5=High) of each film for all respondents: A=3.1, B=4.3, C=2.9
TYPE OF ------------------- MEASURES -------------------------
QUESTION SCALE CENTRAL TENDENCY DISPERSION
1
2
3
What type(s) of tabular/graphical representation would you use to display the responses for each question (table, pie chart, bar chart, line chart, etc.), and why? (3 points each)
QUESTION GRAPHICAL REPRESENTATION REASONS
1
2
3
3. Determine the probability of a normally distributed data point being in the ranges indicated in the following two cases:
a. Between z = 0.54 and z = 2.21
b. Greater than z = 1.05 or less than z = -0.70
c. Exactly equal to z = 1.05
4. For the population of all U.S college students, the GPA is approximately normally distributed,
with a mean of 2.65 and standard deviation of 0.35. Find the following:
a. The upper and lower levels of the GPA that include 2/3 of all grades (assume the upper
and lower levels are equidistant above and below the mean)
b. The probability that a student has a GPA of at least a "B+" (i.e., at least 2.80)
5. Given the equation y = 2x + 4, answer the following questions:
a. What type of equation is this?
b. What is the independent variable?
c. What is the dependent variable?
d. What term do we use for the "2", and what does it mean?
e. What term do we use for the "4", and what does it mean?
f. Graph this equation using its (x,y) coordinates
g. If the equation resulted from a regression analysis involving a set of ten (x,y) data points:
(1) What is the value of y when x = 4?
(2) If r = 0.80, what is the "goodness of fit" of the equation with the data points?
(3) What suggestions would you make to improve the "goodness of fit"?
(4) How does "goodness of fit" relate to the confidence level for the equation?
h. If the two variables were disposable income and building permits, which would be the independent variable and which the dependent variable? State your reasons.
i. If the two variables were interest rates and mortgage re-financings, would you expect the correlation coefficient (r) to be positive or negative? State your reasons.
j. How can regression analysis be used in business operations and future planning?
6. What hypothesis test(s) would you apply to the following four situations and specify your reasons why (measurement scale/data type, sample number/type/size, etc.)
A. The Republican party suspects there are geographical differences regarding five issues.
The importance of each issue is based on ratings (1=low to 5=high) gotten from telephone interviews of 100 people each in Atlanta, Dallas, Indianapolis and New York City.
B. The Democratic Party believes the Atlanta Mayor's performance has declined. A random sample of 200 Atlanta residents were surveyed and asked to respond with "Yes", "No" or "No opinion" on four issues for which survey results had been reported one year ago.
C. To understand differences in viewer preferences for pilot TV programs, NBC surveys 300 viewers each in Atlanta and Miami and gets rankings (1, 2 or 3) of their preferences.
D. ABC, Inc. hires new salespeople based on the scores on an entrance test. The salespeople attend a two-week training session to improve their knowledge base, and are tested again.
ABC's President wants to know if the salespeople's level of knowledge has increased.
Measurement ---------- Sample description ----------
Case Scale/Data type Number Independent/Related Size Hypothesis test(s)
A
B
C
1. Grokers grocery store has soup sales averaging 2,000 cans per week, with a standard deviation of 200 cans. The cost of a stock-out is four times greater than the cost of being over-stocked. Store management wants to set the upper and lower stocking levels, such that there is a 95% probability that weekly sales will fall between these levels. What are these levels?
2.a. What is the probability of flipping a coin and getting five tails in a row?
2.b. What is the probability of drawing from a card deck:
(1) a King, a Heart, or a one-eyed Jack?
(2) a King, a Heart, and a one-eyed Jack?