Hypothesis Testing and Statistics

The video tutorial explains hypothesis testing using a sample of 27 observations with a mean of 22 and a standard deviation of 4.8. It tests if the population mean is significantly below 24 at a significance level of 0.01. The tutorial covers setting up null and alternative hypotheses, conducting a left-tailed t-test, calculating degrees of freedom, finding the critical value, and computing the test statistic. The conclusion is that there is not enough evidence to reject the null hypothesis, meaning the population mean is not significantly less than 24.

What is the sample size used in the problem?

• 27

• 30

• 24

• 22

What is the significance level (α) used in the test?

• 0.05

• 0.001

• 0.01

• 0.10

What is the sample mean in this problem?

• 24

• 22

• 26

• 20

What is the sample standard deviation in this problem?

• 5.2

• 4.8

• 5.0

• 4.5

What is the alternative hypothesis in this test?

• The mean is greater than 24

• The mean is equal to 24

• The mean is less than 24

• The mean is not equal to 24

What is the null hypothesis in this test?

• The mean is less than 24

• The mean is not equal to 24

• The mean is equal to 24

• The mean is greater than or equal to 24

What type of test is being conducted?

• Left-tailed test

• Two-tailed test

• None of the above

• Right-tailed test

Why is a t-test used in this scenario?

• Because only the sample standard deviation is available

• Because the population mean is known

• Because the sample size is large

• Because the population standard deviation is known

How are the degrees of freedom calculated for this test?

• n

• n - 2

• n - 1

• n + 1

What is the critical value for this one-tailed test at α = 0.01?

• 2.479

• -2.479

• 1.96

• -1.96