Alliant International University

Research II: Data Analysis & Advanced Statistics

Due Date:

Saturday, Mar. 01, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

• (HW_3_1) A manufacturer of disk drives for a well-known brand of computers expects 4% of the drives to malfunction during the computer’s warranty period. Let X be the number of disk drives, in a batch of 10 randomly selected disk drives, which malfunction during this period. X has a Binomial distribution.
• Identify n and p, the parameters of the Binomial random variable.
• In the context of this exercise, state the assumptions required for X to have a Binomial distribution.
• Are the Binomial assumptions satisfied here?
• Calculate the probability that:
1. No disk drive will malfunction during the warranty period.
2. Exactly one disk drive will malfunction during the warranty period.
3. At least two disk drives will malfunction during the warranty period.
4. Between 3 and 6 (inclusive) disk drives will malfunction during the warranty period.

• (HW_3_2) Successful TV advertising depends on being able to get viewers to recall the specific brand being advertised. Two groups of randomly selected students are shown the TV ads for 10 products. One groups saw the TV ads with some sexual content, the other saw the TV ads rated for general audience. One week after seeing the ads each students was asked to name the specific brands which they saw on TV. The mean and SD of the number of correct answers for each group are given in the table below.
• Calculate SE(X1_bar - X2_bar), the standard error of the differences of the sample means for the two groups
• Calculate the two standard error interval for the difference of the two population means m1 - m2
• Write a one paragraph report summarizing your conclusions from the analysis of these data.
 Sexual Content Ads n1=53 X1_bar=7.9 S1=1.82 General Audience Ads n2=60 X2_bar=4.3 S2=1.53

• (HW_3_3) Five fair, but unusual, octahedral (8 face) dice are rolled twice. Let Y be the random variable representing the total sum from this experiment (each die turns up an integer value between 1 and 8). Find the expected value of Y, mY, and the standard deviation of Y, sY.  Suppose, we carry this experiment (rolling five dice twice) 9 times. What would be approximately the distribution of the sample average, Y¯? What are the mean and the standard deviation of the sample average? [Note: Not all types of dice, any number of faces, are possible. For a nice description of which ones that are possible see the following web-page.]