Question

Discuss the basics of Hypothesis Testing. Include an explanation of the following:

(a) The distinction between the p-value method of hypothesis testing and the critical value method of hypothesis testing;

(b) The distinction between a Type 1 error and a Type 2 error.

Answer 1

Answer,

# Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.

a)

Critical values for a test of hypothesis depend upon a test statistic, which is specific to the type of test, and the significance level, α, which defines the sensitivity of the test. A value of α = 0.05 implies that the null hypothesis is rejected 5 % when it is in fact true . Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie and it is quantitative measure.

in other hand ,

P-value is also a quantitative measure for reporting the result of a test of hypothesis.The p-value is the probability of the test statistic being at least as extreme as the one observed given that the null hypothesis is true. A small p-value is an indication that the null hypothesis is false.

b)

Type 1 errors are called" false positives" and it happen in hypothesis testing when the null hypothesis is true but rejected. They happen when the tester validates a statistically significant difference even though there isn’t one.Denoted by “α” correlated to the level of confidence that you set. for example a test with a 95% confidence level means that there is a 5% chance of getting a type 1 error.

in other hand

Type 2 errors are referred to as “false negatives”and type 2 errors happen when the null hypothesis is false and you subsequently fail to reject it. Type 2 error is denoted by “β”.and remember Beta depends on the power of the test .Mathematically ,power=1-β

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