The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical area. Each metropolitan statistical area has at least one urbanized area of 50,000 or more inhabitants. The data in Sheet 10 are the rental vacancy rates (%) for metropolitan statistical area in four geographic regions of the U.S. for the first quarter of 2008. Use alpha = 0.05 to test whether the mean vacancy rate is the same for each geographic region. Sheet 10 Midwest Northeast South West 16,2 2,7 16,6 7,9 10,1 11,5 8,5 6,6 8,6 6,6 12,1 6,9 12,3 7,9 9,8 5,6 10 5,3 9,3 4,3 16,9 10,7 9,1 15,2 16,9 8,6 5,6 5,7 5,4 5,5 9,4 4 18,1 12,7 11,6 12,3 11,9 8,3 15,6 3,6 11 6,7 18,3 11 9,6 14,2 13,4 12,1 7,6 1,7 6,5 8,7 12,9 3,6 11,4 5 12,2 11,5 13,1 4,7 13,6 16,3 4,4 3,3 8,2 3,4 24 5,5 12,2 22,6 12 14,5 12,6 9,5 10,1 Select one: a) Sum of Squares Between Groups = 376.87 > Fcrit = 2.73, reject the null hypothesis, the mean vacancy rate is not the same for four geographic regions b) p-value = 0.0002 < alpha = 0.05, insufficient evidence to reject the null hypothesis, the mean vacancy rate is the same for four geographic regions c) Fstat = 7.41 > Fcrit = 2.73, insufficient evidence to reject the null hypothesis, the mean vacancy rate is the same for four geographic regions d) The ratio of the Mean Square Between Groups and Mean Square Within Groups = 7.41 > Fcrit, reject the null hypothesis, the mean vacancy rate is not the same for four geographic regions
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical area. Each metropolitan statistical area has at least one urbanized area of 50,000 or more inhabitants. The data in Sheet 10 are the rental vacancy rates (%) for metropolitan statistical area in four geographic regions of the U.S. for the first quarter of 2008.
Use alpha = 0.05 to test whether the
Sheet 10
| Midwest | Northeast | South | West |
| 16,2 | 2,7 | 16,6 | 7,9 |
| 10,1 | 11,5 | 8,5 | 6,6 |
| 8,6 | 6,6 | 12,1 | 6,9 |
| 12,3 | 7,9 | 9,8 | 5,6 |
| 10 | 5,3 | 9,3 | 4,3 |
| 16,9 | 10,7 | 9,1 | 15,2 |
| 16,9 | 8,6 | 5,6 | 5,7 |
| 5,4 | 5,5 | 9,4 | 4 |
| 18,1 | 12,7 | 11,6 | 12,3 |
| 11,9 | 8,3 | 15,6 | 3,6 |
| 11 | 6,7 | 18,3 | 11 |
| 9,6 | 14,2 | 13,4 | 12,1 |
| 7,6 | 1,7 | 6,5 | 8,7 |
| 12,9 | 3,6 | 11,4 | 5 |
| 12,2 | 11,5 | 13,1 | 4,7 |
| 13,6 | 16,3 | 4,4 | 3,3 |
| 8,2 | 3,4 | ||
| 24 | 5,5 | ||
| 12,2 | |||
| 22,6 | |||
| 12 | |||
| 14,5 | |||
| 12,6 | |||
| 9,5 | |||
| 10,1 |
b) p-value = 0.0002 < alpha = 0.05, insufficient evidence to reject the null hypothesis, the mean vacancy rate is the same for four geographic regions
c) Fstat = 7.41 > Fcrit = 2.73, insufficient evidence to reject the null hypothesis, the mean vacancy rate is the same for four geographic regions
d) The ratio of the Mean Square Between Groups and Mean Square Within Groups = 7.41 > Fcrit, reject the null hypothesis, the mean vacancy rate is not the same for four geographic regions
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