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- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- RECAP OF PREVIOUS LESSON
- You learned that calculating the sample variance only when the dataset you're working with represents a sample taken from larger population interest. Also, you learned the calculate the population variance when dataset you're working with represents an entire population. Now let's talk about...
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN: VARIANCE IS KNOWN
- When the Population variance is known and the sample size is large, the test statistic appropriate used is z- test. Z-test is used to determine the difference between means of two populations.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN: VARIANCE IS UNKNOWN
- Otherwise, when the Population variance is unknown and have limited sample size, the test statistic appropriate used is t- test. T-test is used to determine a significant difference between two sample groups that are independent in nature.
- Variance is equal to the standard deviation, squared.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM USED
- What is Central Limit Theorem?(CTL) or central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the size of the sample increases, regardless of the shape of the original distribution. Appropriate test statistic in this theorem is z-test.
- REMEMBER:Z-test is the appropriate tool to used in Variance is known when:The population standard deviation (σ) is known.The sample standard deviation (s) is unknown.The population is normally distributedThe sample size is greater than or equal to 30 (n≥30).
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM USED
- We can say that, Central Limit Theorem apply when the sample size is extremely large weather the variance (σ2) is known or unknown. When the sample size are small, the CTL doesn't apply. So you must then impose stricter assumption to give statistical validity to the test procedure.
- REMEMBER:T-test is the appropriate tool to used in Variance is unknown when:The population standard deviation (σ) is unknown.The sample standard deviation (s) is known. The population is normal or nearly normally distributedThe sample size is less than 30 (n30).
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:
- Z-testn ≥ 30, σ is not knownn ≥ 30, σ unknown (Central Limit Theorem)n30, σ is known
- So, That's it for today, I hope you jot down notes important key points of what I discuss. Thank You For listening.. See you on our final exam. Goodbye Class!
- T-testn 30, σ is not knownn ≥ 30, s is known
- T-testn 30, σ is not known
- It is done by replacing population standard deviation with sample standard deviation in the formula =
- If the population is normally distributed or the sample size is large and the true population means μ =o, then z has a standard normal distribution.The sample standard deviation (s) may be used to estimate the population standard deviation (σ) when the value of σ is unknown.If the standard deviation is known then test statistic[( x̅μo / (σ /√n )] has normal distribution
- 5/9/2022
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