The following table summarizes whether the stock market went up or down during each trading day of 2010. (a) Use a chi-squared test to determine if these data indicate that trading on some days is...

The following table summarizes whether the stock market went up or down during each trading day of 2010.

(a) Use a chi-squared test to determine if these data indicate that trading on some days is better or worse (more or less likely to earn positive returns) than any other.

(b) How does the test used in “a” differ from comparing the proportion positive for each day with 0.5?

(c) These data only indicate the direction of the market. How does that limit the conclusions we might draw?

(a) What does the normal quantile plot indicate about the distribution of returns?

(b) The table groups all returns that are less than -0.03 and more than 0.03. Why not use more categories to separate very high or low returns?

(c) Compute the chi-squared test of goodness of fit and its
-value, noting that we have to estimate two parameters from the data in order to find the expected counts.

(d) Does the chi-squared test agree with the normal quantile plot?

(e) What’s the advantage of using a normal quantile plot to check for normality? The advantage of using the chi-squared test?