Grade 11 Math: Hypothesis Testing Worksheet
This worksheet covers fundamental concepts of hypothesis testing, including null and alternative hypotheses, p-values, and types of errors for Grade 11 math students.
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Hypothesis Testing Fundamentals
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Read each question carefully and provide your best answer. Show all your work where applicable.
1. Which of the following statements about the null hypothesis (H₀) is true?
It always states that there is a significant difference.
It is the hypothesis that the researcher is trying to prove.
It represents a statement of no effect or no difference.
It is only used when the sample size is small.
2. What does a p-value less than the significance level (α) typically indicate?
Strong evidence in favor of the null hypothesis.
Insufficient evidence to reject the null hypothesis.
Strong evidence to reject the null hypothesis.
The alternative hypothesis is always false.
3. A Type I error occurs when we the null hypothesis when it is actually .
4. The hypothesis is the statement that there is a difference or an effect, and it is denoted by .
5. A significance level (α) of 0.05 means there is a 5% chance of making a Type II error.
True
False
6. Increasing the sample size generally decreases the probability of both Type I and Type II errors.
True
False
7. A company claims that the average lifespan of its light bulbs is 1000 hours. A consumer group suspects it's less. Formulate the null and alternative hypotheses for this scenario.
8. Explain in your own words what a 'p-value' represents in the context of hypothesis testing.
9. Consider a scenario where we are testing if the mean height of students in a school is different from the national average of 160 cm. The distribution of heights is approximately normal. Draw a conceptual normal distribution curve and shade the critical region for a two-tailed test with a significance level of α = 0.05.
10. A pharmaceutical company develops a new drug to lower blood pressure. They claim that the drug reduces systolic blood pressure by an average of 15 mmHg. A study is conducted with 50 patients, and the average reduction observed is 13 mmHg with a standard deviation of 5 mmHg. At a 0.01 significance level, can we conclude that the drug's effect is less than claimed? State your hypotheses, identify the type of test, and explain the steps you would take to reach a conclusion (you do not need to perform numerical calculations).