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Statistics

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The mean IQ for a population is 100, and the standard deviation is 15. Girard’s IQ is 142. Given the percentage of people with IQs as high as or higher than Girard’s in this population, does it seem like Girard’s IQ is high enough to reject the null hypothesis? Please justify?
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The basic z score formula for finding a zscore for a sample is:
z = x – μ / σ
When you have multiple samples and want to describe the standard deviation of those sample means, you would use this z score formula:
z = x – μ / (σ / √n)
This z score will tell you how many standard errors there are between the sample mean and the population mean.
Sample problem: In general, the mean height of women is 65″ with a standard deviation of 3.5″. What is the probability of finding a random sample of 50 women with a mean height of 70″, assuming the heights are normally distributed?
z = x – μ / (σ / √n)
= 160 – 142 / (15/√100) = 18 / 150 = 0.12
We know that 99% of values fall within 3 standard deviations from the mean in a normal probability distribution. Therefore, Girard’s IQ is high enough to reject the null hypothesis.
Please let me know if you need any clarification. I'm always happy to answer your questions.
This can also be done using fvalue and pvalue
for further details you can also read this
http://www.statisticshowto.com/fvalueonewayanovarejectnullhypotheses/
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