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Topic: Hypothesis Testing
Example:
Suppose we want to test whether a new drug is effective in reducing cholesterol levels. We randomly select 100 participants and administer the drug to the treatment group while giving a placebo to the control group. After 6 weeks, we measure the cholesterol levels in both groups and compare the means.
Exercises:
- A survey found that 60% of people in a certain city prefer tea over coffee. In a random sample of 200 residents, what is the probability that at least 120 prefer tea?
- A manufacturer claims that the average lifespan of their light bulbs is at least 1000 hours. A sample of 50 bulbs has an average lifespan of 980 hours with a standard deviation of 120 hours. Is there enough evidence to support the manufacturer's claim? Use a significance level of 0.05.
Answers for the exercises above:
- Using the binomial probability formula, we can calculate the probability of at least 120 people preferring tea as 0.0199.
- We can conduct a one-sample t-test to determine if the sample mean differs significantly from the claimed average lifespan. The t-statistic is -1.67, which does not fall in the rejection region at a significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the manufacturer's claim.
Other Resources:
- 作者:现代数学启蒙
- 链接:https://www.math1234567.com/article/statistics
- 声明:本文采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。
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