A calendar effect is an effect on investment returns, particularly in the stock market, that occurs over calendar cycles. An example is the January effect, which describes the rise in stock returns in January compared to other months. Another example is the weekend effect, which refers to the tendency of stocks to show lower returns on Monday than Friday.

Suppose you are a financial analyst. You conduct a hypothesis test to determine whether the mean monthly return for stocks in October is lower than the mean monthly return for stocks in the other months. Assume that the mean monthly return for stocks in the other months is 1.3 percentage. You obtain a sample of October monthly returns for 1,792 stocks for the period 1951-2000, which yields a sample mean of x = 0.4 percentage.

Let mu denote the mean monthly return for stocks in October. Formulate your null and alternative hypotheses by selecting the appropriate values in the blue dropdown menus that follow. H_o: H_a: The test you conduct is test.