What role does sample size play in the mean of the distribution?
As sample size increases, the sampling distribution more closely approximates the normal distribution, and the spread of that distribution tightens.
What makes a sample normally distributed?
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed.
What does the uniform distribution mean for Smiling Time?
This means that any smiling time from zero to and including 23 seconds is equally likely. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. Let X = length, in seconds, of an eight-week-old baby’s smile.
Which is an example of a uniform distribution?
The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. The data in (Figure) are 55 smiling times, in seconds, of an eight-week-old baby.
How does sample size affect the sample mean?
Sampling from the same population with different sample sizes will result in different measures of spread in the outcome distribution. As we expect, increasing the sample size will reduce the standard error and therefore, the distribution will be narrower around its average.
When to use t distribution for sample size?
If the sample size is between 15 and 40, the t-distribution can be used as long as X is unimodal and reasonably symmetric. For sample sizes greater than 40, the t-distribution can be used unless X’s distribution is heavily skewed.