Question

Suppose that you have been following the financial news for the past year-and-a-half, and that you have noticed in particular that the stock markets have shown a great deal of volatility in response to the US government’s efforts to reduce inflation by increasing the Federal lending rate 9 times since the beginning of 2022. Volatility in the market is reflected by an increased variance. If the historical variance of the DOW is known to be 2718 points, and you believe that for the past 1.5 years the DOW has shown increased volatility, write out the appropriate null and alternative hypotheses that you would use to test your belief.

Answer 1

To test the belief that the DOW has shown increased volatility, the null hypothesis would state the variance is equal to the historical figure (H0: σ^2 = 2718), and the alternative hypothesis would suggest the variance has increased (Ha: σ^2 > 2718). A chi-square test for variance would be used to assess this.

Step-by-step explanation:

If we wish to test the belief that the DOW has shown increased volatility over the past year-and-a-half in response to several rate hikes by the US government aimed at reducing inflation, we would formulate the following null and alternative hypotheses:

1. Null hypothesis (H0): The variance of the DOW has not increased and is equal to the historical variance of 2718 points. (Formally, H0: σ^2 = 2718)
2. Alternative hypothesis (Ha): The variance of the DOW has increased, that is, it is greater than the historical variance of 2718 points. (Formally, Ha: σ^2 > 2718)

In this scenario, we would typically use a chi-square test for variance to determine if there is a statistically significant increase in the DOW's variance from its historical value. If the test statistic calculated from the sample data is greater than the critical value from the chi-square distribution, we would reject the null hypothesis in favor of the alternative hypothesis.