For an IQ test, we know the population _ 5 100 and the _X 5 16. We are interested in creating the sampling distribution when N 5 64. (a) What does that sampling distribution of means show? (b) What is the shape of the distribution of IQ means and the mean of the distribution? (c) Calculate _X for this distribution. (d) What is your answer in part (c) called, and what does it indicate? (e) What is the relative frequency of sample means above 101.5?
If you cannot put the symbols in clearly, spell out the names for the concepts.
What is the relative frequency of sample means above 101.5?
To answer these questions, we need to understand some statistical concepts and formulas. Let's go through them step by step:
(a) The sampling distribution of means shows the distribution of all possible sample means that can be obtained from a population. It represents the variability and characteristics of these sample means.
(b) The shape of the distribution of IQ means can be inferred based on the Central Limit Theorem (CLT), which states that, under certain conditions, the sampling distribution of means tends to be approximately normally distributed, regardless of the shape of the population distribution. Given that the population mean and standard deviation are not provided, we can assume a roughly normal distribution.
(c) To calculate the sample mean (_X) for this distribution, we need the population mean (_ 5 16) and the sample size (N 5 64). We can simply use the formula for the sample mean:
_X = _ (population mean)
Given that _ = 16, the sample mean _X would also be 16.
(d) The answer in part (c) is called the sample mean or the mean of the distribution. It represents the average IQ score for the given sample.
(e) To find the relative frequency of sample means above 101.5, we need to know the standard deviation of the population. However, since the population standard deviation is not provided in the question, it is not possible to determine the exact value. The relative frequency represents the proportion of sample means that fall above a certain value in the distribution. In this case, without the population standard deviation, we cannot calculate the relative frequency above 101.5.
In summary:
(a) The sampling distribution of means shows the distribution of sample means from a population.
(b) The shape of the distribution of IQ means would likely be approximately normally distributed based on the Central Limit Theorem.
(c) The sample mean (_X) for this distribution is 16.
(d) The answer in part (c) is called the sample mean, which represents the average IQ score for the given sample.
(e) The relative frequency of sample means above 101.5 cannot be determined without the population standard deviation.