Good morning class, I'm Joana your teacher in this subject. So for today we're just first going to recall our lesson yesterday about identifying appropriate test statistics involving population mean.
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HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
Is there anyone here in the classroom who can recall the appropriate test to be used when the population variance is unknown?
I can recall that ma'am. When the population variance is unknown, the appropriate test statistic to be used is the t-test.
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HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS UNKNOWN
Okay class, Aira is right. T-test is used when the population variance or standard deviation are not known. Moreover, when the variance is unknown and a sample size is less than 30, we should use t-test statistic assuming that the population is normal or approximately normal.
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HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
Okay next, can someone recall the appropriate test to be used when the population variance is known?
I know that ma'am. When the population variance is known, the appropriate test statistic to be used is the z-test.
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HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:VARIANCE IS KNOWN
Okay Shad your explanation was correct. Z-test is used when the variance is known and either the distribution is normal or sample size is large. In z-test, the sample is assumed to be normally distributed and a z-score is calculated with population parameters such as population mean and population standard deviation.
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HOW TO DETERMINE THE APPROPRIATE TOOL WHEN:CENTRAL LIMIT THEOREM
Okay after this last question, we will proceed to our new lesson. Shariena can you explain when do we used Central Limit Theorem?
Yes ma'am. In Central Limit Theorem (CLT) the population is normally distributed or the sample size is large and the true population mean μ =μo, the z has a standard normal distribution. In addition, when the Central Limit Theorem is used, the appropriate test statistic to be used is the z-test by replacing population standard deviation (σ) by sample standard deviation (s) in the formula.