Chi Square Distribution Test of a Single Variance or Standard Deviation

TL;DR

A professor tests if the standard deviation of exam scores in a college math department is less than 8.6 using a sample of 20 scores. The test results do not provide enough evidence to reject the null hypothesis.

Transcript

in this video we're going to talk about how to perform a hypothesis test with a single variance given a chi-square distribution so in this problem the standard deviation of exam scores in the math department of a local college is 8.6 a professor believes this value to be less he samples 20 exam scores and find that the standard deviation is 6.9 doe... Read More

Key Insights

• 🏆 Hypothesis tests can be performed to investigate if a population parameter is significantly different from a hypothesized value.
• 🍸 The choice of one-tailed or two-tailed tests depends on the directionality of the alternative hypothesis.
• ⚾ The critical value is determined based on the desired level of significance and the degrees of freedom.
• 🥺 Calculated chi-square values falling in the rejection region lead to the rejection of the null hypothesis.

Summary & Key Takeaways

• A professor believes the standard deviation of exam scores in a math department is smaller than 8.6.

• The professor samples 20 exam scores and finds a standard deviation of 6.9.

• By performing a hypothesis test using a chi-square distribution, it is determined that the sample does not provide enough evidence to suggest that the true standard deviation is less than 8.6.