How can the normal distribution be used to test hypotheses about populations? Also, how might you surmise that you can use this logic to test a hypothesis such as caffeine improves memory in the caffeine study.

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SoosteethicU · Accepted Answer

Step 1   The normal distribution can be used to test hypotheses about populations when the population is normally distributed or the sample taken from the population is large enough so that it shows the characteristics of the population.   When the sample size is more than 30, usually z-test is used, along with the known population standard deviation. The z-test can be used to differentiate between two population on the basis of their means or proportions. In these cases, both the groups need to be independent of each other.   Step 2   To test a hypothesis such as caffeine improves memory in the caffeine study:   In this case, two independent samples can be taken from two different populations, like, one from the population who uses caffeine and other who does not use caffeine. The sample needs to be large enough so that it can a representative of the population. When the sample size is large enough, the sampling distribution will also be nearly normal and then it can be determined by mean and the standard deviation.   Now, the caffeine is provided to one group and other group is used as control. After this, a memory test is conducted to record the observations.   After conducting the test, is case the null hypothesis is rejected, then it can be stated that the intake of caffeine improves the memory.

How can the normal distribution be used to test hypotheses about populations? Al

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