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3. Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approvalprocess is too easy and, as a result, too many drugs are approvedthat are later found to be unsafe. On the other hand, a numberof industry lobbyists have pushed for amore lenient approval process so that pharmaceutical companies canget new drugs approved more easilyand
quickly. Consider a nullhypothesis that a new, unapproveddrug is unsafe and an alternativehypothesis that a new,
unapproved drug is safe. (8%)
a. Explain the risks of committinga Type I or Type II error.
b. Which type of error are the consumer groups trying to avoid?Explain.
c. Which typeof error are the industry lobbyiststrying to avoid? Explain.
考点：第9章-假设检验-单样本检验，基础概念。（8分）
读题：
零假设H0: 未经批准的新药是不安全的 & 备择假设H1：未经批准的新药是安全的。
SOLUTION：
a. （见书9.1）
a) A Type I error occurs ifyou reject the null hypothesis, H0 (that a new, unapproved drug is unsafe),when it is true and should not be rejected. A Type I error is a “false alarm.”The probability of a Type I error occurring is α.
b) A Type II error occurs ifyou do not reject the null hypothesis, H0 (that a new, unapproved drug isunsafe), when it is false and should be rejected. A Type II error represents a“missed opportunity” to take some corrective action. The probability of a TypeII error occurring is β.
b. The consumer groups are trying toavoid is Type I error. Since as a consumer, you always want to take drugs thatare tested and proved safe. Incorrectly reject H0 when it is true (Type Ierror) would make yourself suffer from increased risk and/or danger.
c. The industry lobbyists are trying to avoid is Type II error. Since asindustry lobbyists, you expect that new drugs can be on sale and make profits.Unsuccessfully reject H0 when it is false (Type II error) would enlarge yourcosts.
4. The file contains the life (in hours) of a sample of 40 100-watt light bulbs producedby Manufacturer A and asample of 40 100-watt light bulbs produced by Manufacturer B. The followingtable shows these dataas a pair of ordered arrays: (8%)
a. Construct afrequency distribution and a percentage distributionfor each manufacturer, using thefollowing class intervalwidths for each distribution:
Manufacturer A: 650 but lessthan 750, 750 but less than 850, andso on. 起点：650，组间距：100
Manufacturer B: 750 but less than 850, 850 but less than 950, andso on. 起点：750，组间距：100
b. Construct cumulative percentage distributions. 要求123…
c. Which bulbs have a longerlife—thosefrom Manufacturer A or Manufacturer B? Explain.
.22 (a) Bulb Life Percentage, Percentage,
(hrs) Mfgr A Mfgr B
650–749 7.5% 0.0%
750–849 12.5 5.0
850–949 50.0 20.0
950–1,049 22.5 40.0
1,050–1,149 7.5 22.5
1,150–1,249 0.0 12.5
(b) Percentage Less Percentage Less
% Less Than Than, Mfgr A Than, Mfgr B
750 7.5% 0.0%
850 20.0 5.0
950 70.0 25.0
1,050 92.5 65.0
1,150 100.0 87.5
1,250 100.0 100.0
(c) Manufacturer B produces bulbs with longer lives than Manufacturer A.
The cumulative percentage for Manufacturer B shows that 65% of its
bulbs lasted less than 1,050 hours, contrasted with 92.5% of Manufacturer
A’s bulbs. None of Manufacturer A’s bulbs lasted at least 1,150 hours, but
12.5% of Manufacturer B’s bulbs lasted at least 1,150 hours. At the same
time, 7.5% of Manufacturer A’s bulbs lasted less than 750 hours, whereas
none of Manufacturer B’s bulbs lasted less than 750 hours.
考点：作图；第8章-置信区间估计（8分）
SOLUTION：
a. 绘制直方图
b. 绘制累计分布图
c. 两样本的均值检验：进行均值的t非配对检验
| Items | Obs | Frequency |
[650,750] | 684,697,720 | 3 |
[750,850] |
|
|
|
|
|
| Items | Obs | Frequency | Percent |
[650,750] | 684,697,720 | 3 | 3/40 |
[750,850] |
|
|
|
|
|
|
|
| Items | Obs | Percent | cumulative percentage |
[650,750] | 684,697,720 | 3/40 | 3/40 |
[750,850] |
| x | 3/40+x |
|
| y | 3/40+x+y |
|
| … | … |
|
| z | 3/40+x+y+…+z=100% |
Total 合计 | 空着 | 100% |
|
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