Problem 1 - A study conducted in September and October of 2010 found that more than half of employers who hired new college graduates last academic year are likely to do so again. (The Wall Street Journal, November 29, 2010). The study showed hiring intentions of the employers to be:
Definitely Hire Likely to Hire Hire Uncertain Will not Hire Total
37% 17% 28% 18% 100%
Six months later, a sample of 500 employers were asked their hiring intentions and gave the following responses:
Definitely Hire Likely to Hire Hire Uncertain Will not Hire Total
170 100 120 110 500
Test to determine whether the proportions from the initial study have changed (Goodness of Fit - Unequal Proportions Test).Use α = .05.
Problem 2 - Given the following contingency table, conduct a difference in proportions test, assuming equal proportions. Use 5% significance level.
|
Group 1
|
|
Group 2
|
1
|
2
|
|
1
|
23
|
47
|
|
2
|
32
|
53
|
Problem 3 - U.S. market share for smartphones with larger screens is increasing. As of the first quarter of 2011, smartphones with screens 4 inches or larger had captured 24% of the smartphone market. The market for smartphones with screens between 3.5 and 3.9 inches has stayed fairly steady at 40%, while that for smartphones with screens less than 3.5 inches has declined to 36%. Does smart phone ownership by college students follow this national pattern? A sample of 148 student smartphone users showed the 30 owned a smartphone with a large screen (4 inches or greater), 75 owned a smartphone with a medium-sized screen (between 3.5 and 3.9 inches) and 43 owned a smartphone with a small screen (less than 3.5 inches). Conduct a Chi-Square goodness of fit test (unequal) to answer this research question using a .05 level of significance.
Problem 4 - A recent study by a large retailer designed to determine whether there was a difference between the importance a store manager placed on advertising and the size of the store revealed the following sample information:
|
|
Important
|
Not Important
|
|
Small
|
40
|
52
|
|
Medium
|
106
|
47
|
|
Large
|
67
|
32
|
Using the Chi-Square test for equality between proportions method of hypothesis testing, is there a difference in importance of advertising based on store size? Hint: The hypothesis will include 3 proportions. Use the .05 significance level. Show all work.