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Statistical Inference-Quiz 3
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Consider the following image, which shows the distribution of sample means of student test scores as predicted by the Central Limit Theorem.
1. In the picture, what is the correct interpretation of the probability of 9.0%? (Choose all that apply)
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1 point
If the population mean is 9.6 and the SD is 3.4, then if I randomly sample 25 students I have a 9.0% chance of my sample mean being greater than 10.5.
9.0% of the area under the curve is above 10.5.
There is a 9.0% chance that the true population mean is 9.6.
If the population mean is 9.6 and the SD is 3.4, then if I randomly sample 25 students I have a 9.0% chance of my sample mean being less than 8.7.
If the population mean is 9.6 and the SD is 3.4, then if I randomly sample 25 students I have a 9.0% chance of my sample mean being less than 10.5.
Required
2. If the sample increased from 25 to 50 students, but the sample mean was still 10.5, which of the following would happen? (Choose all that apply)
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1 point
The area of the curve above 10.5 would be larger.
The probability would fall.
The area of the curve above 10.5 would be smaller.
The probability based on parametric assumptions (i.e. using the Central Limit Theorem to calculate the probability) would be farther from the true probability.
The probability would increase.
The probability based on parametric assumptions (i.e. using the Central Limit Theorem to calculate the probability) would be closer to the true probability.
Required
3. According to the Central Limit Theorem, if the true mean is 9.6 and the standard deviation is 3.4, what is the probability that my random sample of 25 students has a sample mean of 15 or greater?
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1 point
Exactly 0%; it never happens
Between 0% and 9.0%, not inclusive
Between 9.0% and 100%, not inclusive
Exactly 100%
Impossible to say without knowing the standard error
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