6. Statistical Inference

Hypothesis Testing — Quiz

Test your understanding of hypothesis testing with 5 practice questions.

Practice Questions

Question 1

A researcher is investigating if a new drug affects blood pressure. The null hypothesis ($H_0$) is that the drug has no effect, and the alternative hypothesis ($H_1$) is that the drug changes blood pressure. A sample of $50$ patients shows a mean change in blood pressure of $-5$ mmHg with a standard deviation of $10$ mmHg. If the significance level ($\alpha$) is $0.05$, and the calculated Z-score is $-3.54$, what is the correct decision regarding the null hypothesis, given that the critical values for a two-tailed test are $Z_{critical} = \pm 1.96$?

Question 2

A company claims that its new battery lasts for an average of $100$ hours. A consumer group believes the average lifespan is different from $100$ hours. A sample of $36$ batteries yields a sample mean lifespan of $98$ hours and a sample standard deviation of $6$ hours. Calculate the test statistic (t-score) for this hypothesis test.

Question 3

Which of the following scenarios would most appropriately use a two-tailed hypothesis test?

Question 4

A pharmaceutical company claims that a new drug reduces blood pressure by an average of $10$ mmHg. A researcher wants to test if the average reduction is *less than* $10$ mmHg. A sample of $64$ patients shows an average reduction of $8$ mmHg with a standard deviation of $4$ mmHg. Calculate the test statistic (Z-score) for this hypothesis test.

Question 5

What is the effect of decreasing the significance level ($\alpha$) on the probability of a Type I error and the power of a hypothesis test?