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An IQ test is designed so that the mean is 100 and the standard deviation is 10 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with ​99% confidence that the sample mean is within 8 IQ points of the true mean. Assume that σ=10and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is

Respuesta :

Answer:

sample size = 10

it is not practical because we can't draw a conclusion for a complete population based on the sample size of 10 people

Step-by-step explanation:

mean = 100

standard deviation = sigma = 10

confidence level = 99%

The z-score for 99% confidence level = z = 2.58

mean IQ is within 8 IQ points so:

error = E = 8

sample size = n (we don't know it)

Since the distribution is normal, we can use the formula of margin of error for z-distribution to calculate the missing sample size:

[tex]E = z * \frac{sigma}{\sqrt{n} } \\\sqrt{n} = z * \frac{sigma}{E} \\\\\sqrt{n} = 2.58*\frac{10}{8} \\\\\sqrt{n} = \frac{25.8}{8} \\\\n = (\frac{25.8}{8} )^{2}\\n = 10.4\\[/tex]

next integer rounded is 10

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