The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as follows: Ethnicity Number of Cases Percentage of total county population Number of cases expected (round to 2 decimal places) White 2229 42.9% 1748.18 Hispanic 1157 26.7% 1088.03 ? Black/African-American 457 2.6% 0.106 ? Asian, Pacific Islander 232 27.8% 1132.85 ? Total = 4075 Total = 100% Total = 3969.166 ? Perform a goodness-of-fit test to determine whether the make-up of AIDS cases follows the ethnicity of the general population of Santa Clara County. a. What is the null hypothesis? b. What is the alternative hypothesis? c. Is this a right-tailed, left-tailed, or two-tailed test?
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 following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as follows:
|
Ethnicity |
Number of Cases |
Percentage of total county population |
Number of cases expected (round to 2 decimal places) |
|
White |
2229 |
42.9% |
1748.18 |
|
Hispanic |
1157 |
26.7% |
1088.03 ? |
|
Black/African-American |
457 |
2.6% |
0.106 ? |
|
Asian, Pacific Islander |
232 |
27.8% |
1132.85 ? |
|
|
Total = 4075 |
Total = 100% |
Total = 3969.166 ? |
Perform a goodness-of-fit test to determine whether the make-up of AIDS cases follows the ethnicity of the general population of Santa Clara County.
a. What is the null hypothesis?
b. What is the alternative hypothesis?
c. Is this a right-tailed, left-tailed, or two-tailed test?
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