Question

The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1,000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re investment of dividends. Ratings are assigned by dividing all 1,000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one-year ratings for a sample of 60 of the largest companies. A B C D E 5 8 15 20 12 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =

Answer 1

The test statistic can be calculated using the formula and the observed and expected frequencies. The p-value can be found by determining the area under the curve for the test statistic.

Step-by-step explanation:

The test statistic can be calculated by using the formula: test statistic = (observed frequency - expected frequency) / square root of expected frequency. In this case, the observed frequencies are: A = 5, B = 8, C = 15, D = 20, E = 12. The expected frequencies can be calculated by dividing the total number of companies (60) by the number of groups (5). The expected frequency for each group would be 60 / 5 = 12.

Plugging in the values, we get: test statistic = (5 - 12) / square root of 12 = -7 / 3.464 = -2.02 (rounded to three decimal places).

To find the p-value, we can use a chi-square distribution table. The p-value is the probability that the test statistic would be as extreme as the observed result or more extreme, assuming the null hypothesis is true. In this case, since the observed result is in the lower tail, we are looking for the area under the curve to the left of the test statistic.

The p-value for a test statistic of -2.02 can be found in the chi-square distribution table or using a statistical software. The p-value is approximately 0.0433 (rounded to four decimal places).

Answer 2

Measuring stock market performance involves various indices, like the Dow Jones Industrial Average and the S&P 500, which are key to understanding stock price movements. The question mentioned proposes calculating a test statistic and p-value based on a ratings distribution, but lacks detailed context for a precise calculation.

Step-by-step explanation:

Understanding how we measure stock market performance is crucial before diving into the specifics of why stock prices fluctuate. The Dow Jones Industrial Average is one of the most recognized performance measures, which is focused on the stock prices of 30 significant U.S. companies. Another important gauge is the Standard & Poor's 500 (S&P 500), which follows the stock prices of the 500 largest U.S. companies. Meanwhile, the Wilshire 5000 encompasses the stock prices of nearly all publicly traded U.S. companies.

The question about companies' ratings in the Wall Street Journal's Shareholder Scoreboard involves using the notion of total return on stocks, which accounts for both stock price appreciation and the reinvestment of dividends. While the question asked for the calculation of a test statistic and p-value, based on a distribution of 60 companies' ratings, specifics such as the assumed null hypothesis, the expected frequencies for each category, and whether this is a goodness-of-fit Chi-squared test, are needed to provide a numerical answer. Without this information, the exact calculations for the test statistic and p-value cannot be accurately determined.