Week 3 Theoretical Questions Flashcards
What is the role of sampling distribution in statistical inference?
The sampling distribution of a statistic under the null hypothesis informs us how the value of the statistic would vary across random samples if the null hypothesis is correct. According to the distribution and given a value of the statistic computed from a sample, the probability of the statistic taking a value at least as extreme as the one computed from the sample can be derived. We use this probability (p-value) as evidence to reject or accept the null hypothesis.
Which statistic’s sampling distribution does Central Limit Theorem (CLT) prescribes?
CLT is about the sampling distribution of sample mean.
What is the distribution?
It shows that the sampling distribution of the mean of a random sample drawn from a population is approximately normally distributed with mean equal to the population mean and variance equal to the population variance divided by the sample size.
For CLT to be applicable, does the population need to be normally distributed?
It does not require the population to be normally distributed.
What’s the common requirement of the sampling process for CLT to be applicable?
CLT actually applies to any population. One common requirement is that the sample size should be large enough (n≥30). The larger the sample size, the more closely the sampling distribution resembles a normal distribution.
Describe the relationship between rejection region and p-value.
Rejection region and p-value are two ways to present the same statistical evidence in a sample to accept or reject the null hypothesis.
What merits does p-value has compared to rejection region?
P-value can more intuitively show the strength of the statistical evidence regardless of which sampling distribution is involved: the smaller a p-value is, the stronger the evidence is.
Which test is for making inference about single population variance?
A χ^2 test is used to make inference about one population variance.
We know variance is always nonnegative, how is that related to the sampling distribution of the relevant test statistic?
The sampling distribution involved is accordingly a χ^2 distribution. Since variance is always nonnegative, the appropriate sampling distribution function should always be nonnegative, which is one feature of a χ^2 distribution.
(If you remember from Khan Academy the Chi-distribution was only to the right side not a bell shape, only positive values)
When can the Z-test statistic be used?
When the population standard deviation is known. Or when the sample size is larger than 30. Then the t and z scores should be pretty similar. (Not sure if allowed in the test)
