**Hypothesis Testing & Variance**

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•(1) Explain when to use a t-test and when to use a z-test. Explore the differences. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

•(2) Discuss why samples are used instead of populations. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(1) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

The z- test and t- test are basically the same; they compare two means to suggest whether the two samples come from the same population. These tests can also be used to examine whether the mean has a specified value. There are variations in the t- test. If you have a sample and wish to compare it with a known mean the single sample t- test is available. If your samples are not independent of each other and have some factor in common, i.e. geographical location or before/after treatment, the paired sample t- test can be applied. There are also two variations on the two sample t- test, the first uses samples that do not have equal variances and the second uses samples whose variances are equal. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

A z- test is applicable if the data satisfies the following conditions: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(a) The data points should be independent of each other | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(b) The sample size, n > 30 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(c) If n < 30, the distribution should be normal. (If n > 30 the distribution of the data does not matter) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(d) Random sampling | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

A t- test is applicable if the data satisfies the following conditions: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

(a) The data sets should be independent from each other except in the case of the paired-sample t- test |

**Category:**Business, General Business

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