Determine the appropriate hypothesis test(s) to be used in four research projects described below. In selecting the appropriate test(s), you should describe the test selection procedure, considering the following:
- Null hypothesis (H0) and alternative hypothesis/hypotheses (HA)
- Measurement scale/data type: nominal, ordinal, interval or ratio
- Sample description
- Number of samples: 1, 2, or 3 or more
- If samples are independent or related
- Hypothesis test(s) to be used
Describe any other issues/assumptions that should be considered. In some cases, more than one test may apply.
Q1. Five thousand randomly-selected MBA graduates were surveyed to determine their future plans. The survey response rate was 10%. The graduates' future plans were grouped into four categories for each of three majors, as shown in the following table:
-------------- MAJOR (Number of Graduates) ---------------
FUTURE PLANS Marketing (204) Finance (172) Operations (124)
Continue their education 26% 21% 24%
New position - existing company 39% 38% 41%
New position - different company 23% 28% 26%
Not sure 12% 13% 9%
The Business School Dean wants to determine if the future plans are significantly different for the three majors at a level of confidence of at least 90%. What test(s) would you recommend?
Q2. A company hired 20 salespeople and gave them an initial sales skills examination; test scores ranged from 68 to 95, with a mean of 79.4. All salespeople then attended a two-week training program and were re-tested; test scores ranged from 65 to 98, with a mean score of 83.2. The Corporate Training Director asked the Manager of Corporate Research whether the differences in the two test scores was significant, Due to EEO and other regulations, a confidence level of 99% is necessary. What hypothesis test(s) would you suggest to the Manager of Corporate Research?
Q3. An automobile manufacturer markets the same vehicle in Europe and the U.S., but buyer quality ratings are different. Based on a sample of 100 vehicles in each market, a mean quality rating of 4.3 was reported in the U.S. compared to a mean rating of 3.7 in Europe. What test(s) should be used to determine if there is a significant quality difference in the two markets, assuming that a significance level of 5% is required?
Q4. A political party suspects there are differences in Presidential candidate preferences based on age. A nationwide survey was conducted with 500 registered voters selected at random in each of four age groups (30 & under, 31-50, 51-70, over 70). All survey respondents indicated their preference rankings (1, 2, 3) for the party's three leading candidates. To test differences in voting preferences, a significance level of .05 is desired. What test(s) would you recommend?