NOTE: More Problems will be posted on Monday from Chapter 6, 8.1-8.3, and 14.2
 
 

1. Remember the last problem on the midterm?  A company wants to market a product, but only if at least 25% of the market are favorably inclined towards the product.  The give a survey to 50 people from their market, and ask them to score the product with a 1,2, or 3.  A "1" means they would never buy it.  A "2" means they might buy it if it costs $10, and a "3" means they might buy it if it costs $20.   The product will be developed only if 25% of the market would respond with a "2" or "3".  The president is concerned that the survey doesn't ask enough people.   He says, "Let's assume that exactly 25% of the market would answer with a '2' or '3'.  What is the probability, however, that our survey will have less than 25% of the respondants answering with a '2' or '3'?"  In other words, find the probability that their survey will mistakenly conclude that less than 25% of the market would answer with '2' or '3':
a) Design and carry out a 5-step simulation to find the experimental probability of this event.
b) If the sample size were increased to 100, would you expect this probability to increase or decrease? Why?
c) Carry out a simulation to find the exerpimental probability if the survey included 100 people.
d) Write an equation to find the theoretical probability of this event when 50 people are in the survey.
e) Use the STatistics Department Calculators to find the theoretical probability.  (Hint: A CDF is a "cumulative denstity function."  In the discrete case it is related to a PDF as follows: the pdf is P(X=x), where x is whatever value you're interested in, and X is the random variable.  The CDF is
P(X <= x) = sum of all values less than or equal to x of P(X=x).  Another hint for using the calculators: read the directions!)

2. STM: p. 241: 8,9
3. STM: p. 245: 4
4. STM: p. 248: 9
5. STM: p. 579: 7,9  (Note: number 7 has a typo: "lines" should be "times")
6. Children were tested in two different learning styles: active and passive.  A researcher designed two computer programs that presented the same content to children to help them learn "Bliss Symbols".  Bliss Symbols are picto-graphs used to help learning disabled children communicate.  One of the computer programs required the learnings to interact with the computer. These were the "active" learners. The others required that they merely observe the lessons. These were labelled "passive" learners. The children were randomly assigned to either the active or passive group.  At the end of the lesson, they were given an exam. This data set (also available via ActivStats) presents these scores.  Your goal is to determine whether there is a difference in the two groups, and if so, whether that difference could be attributed to just chance.
a) Make a boxplot of the two groups.  Interpret the boxplot.
b) What box model might someone who believed there was a difference use?
c) What box model might a critic use?
d) Write out the 5-step Simulation needed to perform an experimental median test.
e) Carry out the median test.
f) Do you think there was a difference in the two learning styles?