Topic: Hypothesis Testing

Example:

Exercises:

1. 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?

2. 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:

1. Using the binomial probability formula, we can calculate the probability of at least 120 people preferring tea as 0.0199.

2. 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:

• Introduction to Hypothesis Testing

• Statistics for Beginners