Math 225

Introduction to Biostatistics

Solutions to Practice First Midterm

1. True
2. False. The mean does not need to be a possible value.
3. False. The median might not be midway between the maximum and the minimum.
4. False. A quartile is a location. The interquartile range measures spread.
5. False. If two events are mutually exclusive, P(A or B) = 0.
6. False. The probability is (0.5)⁵.
7. True.
8. True.
9. False. For some populations, a larger sample is necessary.
10. A p-value is the probability that a new test statistic would be at least as extreme as the test statistic from the actual observed data assuming that the null hypothesis is true.
11. The probability is 1/7!.
12. Sensitivity = 302/481; Specificity = 372/452. The positive predictive probability is 0.236.
13. (a) 0.2146; (b) 0.1814.
14. (a) 0.3707; (b) 148.2 ounces; (c) 0.2514.
15. (a) (1/2)^6; (b) (2/3)^6; (c) 0.8489.
16. (a) There are at least five observations in each group. (np > 5 and n(1-p) > 5).
    (b) 0.115 ± 0.039 or 0.076 to 0.154.
    (c)

    H₀: p = 0.10
    H_a: p > 0.10
    z = 0.83
    p-value = 0.20; There is little evidence that the five year survival rate exceeds ten percent. The observed rate of 11.5 percent is typical of what might be observed if, in fact, the population five-year survival rate was ten percent. Examining the confidence interval, any population survival rate in the range of 0.076 and 0.154 is a fairly plausible explanation of the data.