Hypothesis Testing Concepts

This tutorial covers hypothesis testing, focusing on a claim by a fitness app about user exercise time. It explains setting up null and alternative hypotheses, conducting a Z-test, and interpreting results using critical regions and P-values. The impact of variability on test outcomes is also discussed.

What is the main purpose of hypothesis testing in statistics?

• To calculate averages

• To collect data

• To make decisions about a population parameter based on sample data

• To prove a theory

What is the alternative hypothesis in the context of the fitness app's claim?

• The average user exercises for 30 minutes or less per day

• The average user exercises for more than 30 minutes per day

• The average user exercises exactly 30 minutes per day

• The average user does not exercise at all

Which type of test is used when the alternative hypothesis suggests a value greater than a certain number?

• Two-tailed test

• Left-tailed test

• No-tailed test

• Right-tailed test

What is the Z-test statistic used for in hypothesis testing?

• To determine the sample size

• To calculate the mean

• To compare the sample mean to the population mean

• To find the standard deviation

What is the critical value in hypothesis testing?

• A type of hypothesis

• A value that determines the sample size

• A threshold to decide whether to reject the null hypothesis

• A measure of variability

What conclusion can be drawn if the Z-statistic is greater than the critical value?

• The null hypothesis is accepted

• The null hypothesis is rejected

• The sample size is too small

• The test is inconclusive

What does a P-value represent in hypothesis testing?

• The probability of the alternative hypothesis being true

• The probability of the sample size being sufficient

• The probability of obtaining an observed effect assuming the null hypothesis is true

• The probability of the null hypothesis being true

If the P-value is less than the significance level, what should be done?

• Reject the null hypothesis

• Accept the null hypothesis

• Increase the sample size

• Decrease the significance level

What happens to the Z-statistic when the population standard deviation increases?

• It decreases

• It becomes zero

• It remains the same

• It increases

How does higher variability affect hypothesis testing?

• It has no effect

• It makes it harder to detect significant differences

• It always leads to rejection of the null hypothesis

• It makes it easier to reject the null hypothesis