Hypothesis Testing with Chi-Square Distribution

This video tutorial explains how to perform a hypothesis test for a single variance using a chi-square distribution. It begins with a problem where a professor suspects the standard deviation of exam scores is less than the known value. The video covers setting up the null and alternative hypotheses, determining the type of test, calculating the critical chi-square value, and using the sample data to compute the chi-square statistic. The conclusion is drawn based on whether the calculated value falls within the rejection region, ultimately deciding if there is enough evidence to reject the null hypothesis.

What is the main focus of this video tutorial?

• Learning about regression analysis

• Understanding the normal distribution

• Calculating the mean of a data set

• Performing a hypothesis test with a single variance using a chi-square distribution

What is the hypothesized standard deviation in the problem?

• 9.2

• 6.9

• 7.5

• 8.6

What is the sample size used in the problem?

• 30

• 20

• 25

• 15

What type of test is being conducted in this hypothesis test?

• None of the above

• Left-tailed test

• Right-tailed test

• Two-tailed test

What is the significance level used in this test?

• 0.01

• 0.05

• 0.15

• 0.10

What is the critical chi-square value for 19 degrees of freedom with an area to the right of 0.95?

• 12.23

• 8.345

• 10.117

• 15.987

What is the formula used to calculate the chi-square value from the sample?

• (n - 1) * (population variance) / (sample variance)

• (n + 1) * (sample variance) / (population variance)

• (n - 1) * (sample variance) / (population variance)

• (n + 1) * (population variance) / (sample variance)

What is the calculated chi-square value from the sample data?

• 10.117

• 6.9

• 12.23

• 8.6

Based on the calculated chi-square value, what decision is made regarding the null hypothesis?

• The decision cannot be made

• Reject the null hypothesis

• Do not reject the null hypothesis

• Accept the null hypothesis

Why is the null hypothesis not rejected in this test?

• The significance level is too high

• The sample size is too small

• The calculated chi-square value is greater than the critical value

• The calculated chi-square value is less than the critical value