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A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. For each significance level, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's t-test which has separate critical values for each sample size. Therefore, many statistical tests can be conveniently performed as approximate Z-tests if the sample size is large or the population variance known. If the population variance is unknown (and therefore has to be estimated from the sample itself) and the sample size is not large (n < 30), the Student's t-test may be more appropriate.

Nuisance parameters should be known, or estimated with high accuracy. Z-tests focus on a single parameter, and treat all other unknown parameters as being fixed at their true values. The test statistic should follow a normal distribution

Z-test and T-test are statistical tests used to determine whether two population means are different. Z- test is applied when the variances are known and the sample size is large (n 30), the standard deviation is unknown while z-tests assume that it is known. Z-test has a single critical value which makes it more convenient than the t-test which has separate critical values for each sample size.

1. Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T-distribution.

2. A T-test is appropriate when you are handling small samples (n < 30) while a Z-test is appropriate when you are handling moderate to large samples (n > 30).

3. T-test is more adaptable than Z-test since Z-test will often require certain…...

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...PREDICTING FINANCIAL DISTRESS OF COMPANIES: REVISITING THE Z-SCORE AND ZETA® MODELS Edward I. Altman* July 2000 *Max L. Heine Professor of Finance, Stern School of Business, New York University. This paper is adapted and updated from E. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” Journal of Finance, September 1968; and E. Altman, R. Haldeman and P. Narayanan, “Zeta Analysis: A New Model to Identify Bankruptcy Risk of Corporations,” Journal of Banking & Finance, 1, 1977. Predicting Financial Distress of Companies: Revisiting the Z-Score and ZETA® Models Background This paper discusses two of the venerable models for assessing the distress of industrial corporations. These are the so-called Z-Score model (1968) and ZETA® 1977) credit risk model. Both models are still being used by practitioners throughout the world. The latter is a proprietary model for subscribers to ZETA Services, Inc. (Hoboken, NJ). The purpose of this summary are two-fold. First, those unique characteristics of business failures are examined in order to specify and quantify the variables which are effective indicators and predictors of corporate distress. By doing so, I hope to highlight the analytic as well as the practical value inherent in the use of financial ratios. Specifically, a set of financial and economic ratios will be analyzed in a corporate distress prediction context using a multiple discriminant statistical methodology.......

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...Z = 1.2X.sub.1 + 1.4X.sub.2 + 3.3X.sub.3 + 0.6X.sub.4 + 1.0X.sub.5 Where X.sub.1 = Working Capital/Total Assets. This measures liquid assets in relation to the firm's size. Altman, interestingly, mentions that the most widely used current and acid ratios were not as good predictors as this measure. Where X.sub.2 = Retained Earnings/Total Assets. This is a measure of cumulative profitability that reflects the firm's age as well as earning power. Many studies have shown failure rates to be closely related to the age of the business. Where X.sub.3 = Earnings Before Income Taxes/Total Assets. This is a measure of operating efficiency separated from any leverage effects. It recognizes operating earnings as a key to long-run viability. Where X.sub.4 = Market Value of Equity/Book Value of Debt. This ratio adds a market dimension. Academic studies of stock markets suggest that security price changes may foreshadow upcoming problems. Where X.sub.5 = Sales/Total Assets. This is a standard turnover measure. Unfortunately, it varies greatly from one industry to another. We take the data from Yahoo Finance for year ended Dec 31, 2007 Sub 1 = Working Capital/Total Assets Current Assets 60,430 Current Liabilities 70,338 Working Capital (9,908) Total Assets 148,883 Sub 1 -6.65% Sub 2 = Retained earnings/Total Assets Retained earnings (39,392) Sub 2 -26.46% Sub 3 = Earnings Before Income Taxes/Total Assets Earnings......

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...Z-Scores A z-score, which is symbolized as z, is the statistic that relates the distance a score is relative to its mean when measured in standard deviation (SD) units (Heiman, 2012). The importance of a z-score is that it enables one to analyze data relative to scores. Z-Scores allow us to determine whether a particular score is equal to the mean, below the mean or above the mean of a bunch of scores, and how far a particular score is away from the mean. Evaluating the scores of Eric’s to determine different z-scores, we use the following computations that he computed where it takes a mean of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to his job. , Next we determine the z-score relative to the mean and the SD, to analyze the difference in time to accomplish these steps on different days. One day it took Eric 21 minutes to get to work, and computing the means from the minutes by the SD results in a z of +1.33, which tells you that Eric's time to get to work is 1.33 standard deviations from the mean. The z is positive because it is above the mean, and demonstrates that it took longer for Eric to leave home, park his car and walk to his job when the raw value of time was 21 minutes. On another day in which it took Eric 12 minutes to get to work, the z value resulted -1.66, demonstrating that the time it took Eric to get to work was below the mean, or it took less time. Observing the time in comparison to the mean, it is......

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...1969), known by his stage name Jay-Z (sometimes stylized as Jay Z or JAY Z),[2][3][4] is an American rapper, record producer, and entrepreneur. He is one of the most financially successful hip-hop artists and entrepreneurs in America. In 2012, Forbes estimated Carter's net worth at nearly $500 million.[1][5] He is one of the world's best-selling artists of all time having sold more than 75 million records, while receiving 17 Grammy Awards for his musical work, and numerous additional nominations.[6][7][8] Consistently ranked as one of the greatest rappers of all time, he was ranked number one by MTV in their list of The Greatest MCs of All-Time in 2006.[9] Three of his albums, Reasonable Doubt (1996), The Blueprint (2001), and The Black Album (2003), are considered landmarks in the genre with all of them featured in Rolling Stone's list of the 500 greatest albums of all time.[10][11][12] As an entrepreneur and investor, Jay-Z co-owns the 40/40 Club, and is the co-creator of the clothing line Rocawear.[13] He is the former president of Def Jam Recordings, co-founder of Roc-A-Fella Records, and the founder of Roc Nation. He also founded the sports agency Roc Nation Sports and is a certified NBA and MLB sports agent.[14] As an artist, he holds the record for most number one albums by a solo artist on the Billboard 200 with 13.[15][16] Jay-Z also has had four number ones on the Billboard Hot 100, one as lead artist. On December 11, 2009, Jay-Z was ranked as the tenth-most......

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