Z-test

Z-TEST -NONPARAMETRIC TESTS- STATISTICS

1. Z - Test Femy moni Assistant professor St. Aloysius college elthuruth

2. INTRODUCTION Statistical test of hypothesis is the test conducted to accept or reject the hypothesis. Commonly used statistical tests are Z-test, t-test, chi-square test, F-test. The decision to accept or reject the null hypothesis is made on the basis of a statistic computed from the sample. Such statistic is known as test statistic (Z, t, F, chi-square). Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Non-parametric tests are “distribution-free” and, as such, can be used for non-Normal variables.

3. Z- TEST Z - test is a statistical tool used for the comparison or determination of the significance of several statistical measures, particularly the mean in a sample from a normally distributed population or between two independent samples. Z - tests are also based on normal probability distribution. Z - test is the most commonly used statistical tool in research methodology. Z - test is a Parametric test.

4. USES OF Z-TEST To test the given population mean when the sample is large (30 or more) or when the population SD is known. To test the equality of two sample means when the samples are large (30 or more) or when the population SD is known. To test the population proportion. To test the equality of two sample proportions. To test the population SD when the sample is large. To test the equality of two sample standard deviations when the samples are large or when population standard deviations are known. To test the equality of correlation coefficients.

5. ASSUMPTIONS Sampling distribution of test statistic is normal. Sample statistics are close to the population parameter and therefore for finding standard error, sample statistics are used in places where population parameters are to be used.

6. STEPS IN CALCULATION Step 1 : Formulate the hypothesis Ho : which is stated for the purpose of possible acceptance. It is the original hypothesis. H1 : hypothesis other than null hypothesis is called alternative hypothesis.

7. Step 2: Deciding the level of significance The level of significance is the probability of rejecting the null hypothesis when it is true, also known as alpha or ' α ' . The commonly used level of significance is either 0.05 or 0.01 . Critical Region The critical region is called the region of rejection.It is the region in which the null hypothesis is rejected. The are of critical region is equal to the level of significance, α.

8. Step 3: Calculation of the value I . Testing The Given Population Mean Ho: There is no significant difference between sample mean and population mean. Formula:

9. II. Testing Equality Of Two Population Means. Ho : There is no significant difference between two means. Formula:

10. III. Testing Population Proportion H0: There is no significant difference between sample proportion and population proportion. Formula:

11. IV. Testing Equality Of Two Proportions Ho : There is no significant difference between two population proportions. Formula:

12. V. Significance Of Difference Between Sample SD And Population SD Ho : There is no significant difference between sample SD and population SD. Formula:

13. VI. Significance Of Difference Between Standard Deviations Of Two Populations Ho : There is no significant difference between two standard deviations. Formula:

14. Step 4: Obtaining the table value and making the decision The table value is obtained from the 'Table values of z for z - test' by locating the level of significance and degree of freedom. For z - test, the degree of freedom is infinity The decision to accept or reject the null hypothesis is made when; Calculated value < Table value = Accept Ho Calculated value > Table value = Reject Ho

15. ADVANTAGES It is a straightforward and reliable test. A Z-score can be used for a comparison of raw scores obtained from different tests. While comparing a set of raw scores, the Z-score considers both the average value and the variability of those scores.

16. DISADVANTAGES Z-test requires a known standard deviation which is not always possible. It cannot be conducted with a smaller sample size (less than 30).