Please help me with this question:
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?
Let say that I have computed value for t is +3.28. The critical value of t is +2.048. How would you explain this? Would the null hypothesis or not? I have a 28 degree of freedom and are using a two tailed non-directional test how cold I illustrate the relationship between the critical and the computed values of t for the result?
To answer your question, let's break it down into parts:
(a) What does the sampling distribution of means show?
The sampling distribution of means shows the distribution of the means of all possible samples of a particular size taken from a population. In this case, we are creating the sampling distribution for an IQ test with a population size of 100 and a sample size of 64.
(b) What is the shape of the distribution of IQ means and the mean of the distribution?
The shape of the distribution of IQ means follows the Central Limit Theorem (CLT), which states that the sampling distribution of means will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is large enough (typically N > 30). The mean of the distribution of IQ means will be equal to the mean of the population, which is given as X = 16.
(c) Calculate X̄ for this distribution.
To calculate X̄ (pronounced "X-bar"), we can use the formula: X̄ = μ, where μ is the population mean. Given that μ = 16, that would be the value of X̄ for this distribution.
(d) What is your answer in part (c) called, and what does it indicate?
The answer in part (c), X̄ = 16, is called the "expected value" or "mean" of the sampling distribution. It indicates that on average, the sample means will be equal to the population mean.
(e) What is the relative frequency of sample means above 101.5?
To determine the relative frequency of sample means above 101.5, we would need additional information such as the standard deviation of the population. Please provide the standard deviation, and I can help you calculate the relative frequency using the Z-score and the standard normal distribution table.