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Sagot :
Using the Central Limit Theorem, it is found that the researcher should use a sample size of 640.
Central Limit Theorem
- The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
- From this, we can take that the standard deviation is inversely proportional to the square root of the sample size.
Hence, for the standard deviation to be cut be half, the sample size has to be multiplied by 4, which means that it should be of 4 x 160 = 640.
To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/25581475
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