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- CENTRAL LIMIT THEOREM
- #160; #160; #160;-When the Population Variance is Unknown, the appropriate test statistic to used is t-test.-What is a t-test? A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features.#160;
- HOW TO DETERMINE THE APPROPRIATE TOOL WHEN
- VARIANCE IS UNKNOWN
- REMEMBER:
- The population standard deviation (σ) is unknown.The sample standard deviation (s) is known.The population is normal or nearly normally distributed.The sample size is less than 30 (n30).
- T-TEST IS THE APPROPRIATE
- VARIENCE IS KNOWN
- HOW TO DETERMINE THE APPROPRIATE TOOL WHENVARIANCE IS UNKNOWN
- when the Central Limit Theorem (CLT) is used, the appropriate test statistic is using z-test by replacing population standard deviation (σ) by sample standard deviation (s) in the formula.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHENCENTRAL LIMIT THEOREM
- Z-testn ≥ 30, σ is knownn ≥ 30, σ is unknown (Central Limit Theorem)n 30, σ is known
- REMEMBER:Z-test is the appropriate tool to used in central limit theorem when:If the population is normally distributed or the sample size is large and the true population means μ = μo, the z has a standard normal distribution.The sample size is extremely large and the variance (σ2) is known or unknown.The sample standard deviation (s) may be used as an estimate of the population standard deviation (σ) when the value of σ is unknown.
- T-testn 30, σ is not knownn ≥ 30, s is known
- A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large.
- A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. A z-test is a hypothesis test in which the z-statistic follows a normal distribution.#160;A z-statistic, or z-score, is a number representing the result from the z-test.
- #160;If the population variance is unknown, which is usually the case, then use a#160;t-test#160;rather than a normal or z-test.
- HOW TO DETERMINE THE APPROPRIATE TOOL WHENVARIENCE IS KNOWN
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