1. A store manager wants to determine if there is a relationship between the day of sale and the price of the item for the number of items sold. The following data was obtained for the price of an item on particular days of the week. What is the expected value for C4.1 ?
Low Medium High
Mon 18 14 3
Tues 14 13 6
Wed 18 19 5
Thurs 27 23 11
Fri 34 27 12
3. Six different brands of popcorn were tested for popping. Two hundred kernels of each brand were popped and the number of kernels that did not pop were counted. Determine the expected value and then plot it on a graph with the observed values.
Brand Number of kernels not popped
A 21
B 13
C 24
D 16
E 12
F 22
4. The dean of a local school wanted to determine if the grade distribution was independent of the subject matter taught. How many degrees of freedom does this contingency table have?
Subject A B C D E
Science 5 11 27 7 11
History 14 18 32 5 7
English 18 35 68 18 23
5. A research firm reported that 15% of those surveyed described their health as poor, 26% as good, 40% as very good, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their health. In a sample of 610 people in Chicago, 70 described their health as poor, 180 as good, 220 as very good, and 140 as excellent. Plot the observed and expected values and calculate the test value.
7. An insurance representative wants to determine if the proportions of women and men who buy the different policy types are the same. The actual sales results for 50 women and 50 men are
Policy A Policy B
Women 20 30
Men 14 36
Under the null hypothesis, what is the expected number of men who would buy Policy B?
13. A software company wants to determine whether there is a relationship between their three sales offices and the sales of their software products. The actual sales results are
Product A Product B Product C
Office 1 17 11 22
Office 2 18 24 8
Office 3 24 11 65
Under the null hypothesis, what is the expected number of Product A that would be sold by Office 2?
18 A researcher is comparing samples from 3 populations. She has 10 samples from the first population and 10 samples from the second population. What is the maximum number of samples she can take from the third population?
19. A portion of an ANOVA summary table is shown below.
Source Sum of Squares Degrees of Freedom
Between 17 4
Within (error) 42 35
Total 59
The critical value for this problem should have dfN (degrees of freedom in the numerator) and dfD (degrees of freedom in the denominator). What would dfN and dfD be?
20 A researcher is comparing samples from 6 different populations. Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means are not all equal. How many of the population means would be significantly different from the others?