This document discusses the t-test and z-test statistical tests. It explains that the t-test is used for small sample sizes (less than 30) when the population standard deviation is unknown, while the z-test is used for large sample sizes (greater than 30) when the population parameter is known. The t-test can test the significance of a single mean, the difference between two independent sample means, or the difference between two dependent/matched sample means. Examples are provided for using the t-test to test the significance of a single mean and the difference between two independent sample means. The z-test is briefly explained as well.

1. T-AND Z-TEST
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2. Learning Objectives
 To understand the meaning of small and large sample
size.
 In which condition, t-test and z-test may be employed
 Practical session on t-test and z-test

3. Quick Overview
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4. Points to consider for t-test
 It is used when sample size is 30 or less than
30.
 The population standard deviation is unknown.
 It is employed under the assumption of a
normally distribution.

5. Application of t-test
1. To test the significance of the mean of a
random sample.
2. Testing difference between means of two
sample (independent samples)
3. Testing difference between means of two
samples (Dependent samples or matched paired
observations)

6. T-static/student t-test
computation
1. To test the significance of the mean of a
random sample.

7. Testing the significance of the
mean of a random sample.
Q1. The manufacturer of a certain make of electric
bulbs claims that his bulbs have a mean life of 25
months with a standard deviation of 5 months. A
random sample of 6 such bulbs gave the following
values:
Life of months: 24, 26, 30, 20, 20, 18
Can you regard the producer’s claim to be valid at
1% level of significance? (Given that the table value
of the appropriate test statistics at the said level are
4.032, 3.707 and 3.499 for 5, 6, and 7 degrees
freedom respectively)

8. Q2:

9. 2.Testing difference between
means of two sample

10. 3. Testing difference between means of two
samples (Dependent samples or matched
paired observations)

11. Z-test
 It is employed when sample size is greater
than 30.
 The population parameter is known.
Where sigma denotes standard deviation of
population.

12. THANK YOU
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