Question

9. Define the following terms or concepts based on your understanding from the book.                                                                                                                                                                                                     8 points

a) Type I and Type II error

b) Statistical Significance and P-value (and what’s the “wrong” interpretation of a p-value?)

c) Critical Region

d) What happens to a normal distribution when the standard deviation increases (but the mean stays the   same)?

Answer 1

a)

type I error :In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding)

type II error :a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding)

b) Statistical significance : In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given thenull hypothesis. More precisely, a study's defined significance level, α, is the probability of the study rejecting the null hypothesis, given that it were true

p-value : The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

c)Critical Region :The set of outcomes of a statistical test for which the null hypothesis is to be rejected

d)The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus the mean of the distribution of the means never changes. The standard deviation of the sample means, however, is the population standard deviation from the original distribution divided by the square root of the sample size. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.