Question

What are the steps in hypothesis testing?

What is the goal of hypothesis testing?

What are null and alternative hypotheses?

In §9.2 the concepts of Type I and Type II errors are introduced.Consider the situation where a husband and wife go to the doctor’s office to each get some tests run and the doctor accidentally mixes up their charts. The doctor comes into the exam room with the results of the tests and declares that the wife is NOT pregnant but her husband IS indeed pregnant with a baby.

How does this illustrate the concepts behind Type I and Type II errors?  Make sure to state your null hypothesis for this situation when discussing error.

Answer 1

Solution: These are steps in the process of hypothetical testing

1. The first step is to specify the null hypothesis. For a two-tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions. A typical null hypothesis is   which is equivalent to  . For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero. If the prediction is that   is greater than then the null hypothesis is .

2. The second step is to specify the   level which is also known as the significance level . Typical values are 0.01,0.05,0.10

3. The third step is to compute the probability value (also known as the p value). This is the probability of obtaining a sample statistic as different or more different from the parameter specified in the null hypothesis given that the null hypothesis is true.

4. Finally, compare the probability value with the α level. If the probability value is lower then you reject the null hypothesis. Keep in mind that rejecting the null hypothesis is not an all-or-none decision. The lower the probability value, the more confidence you can have that the null hypothesis is false. However, if your probability value is higher than the conventional α level of 0.05, most scientists will consider your findings inconclusive. Failure to reject the null hypothesis does not constitute support for the null hypothesis. It just means you do not have sufficiently strong data to reject it.

The goal of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter.

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis (H0)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

Alternative Hypothesis (H1)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

Type I error

When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. To lower this risk, you must use a lower value for α. However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists.

Type II error

When the null hypothesis is false and you fail to reject it, you make a type II error. The probability of making a type II error is β, which depends on the power of the test. You can decrease your risk of committing a type II error by ensuring your test has enough power. You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

considering two hypothesis for two claim

1. Woman is not pregenant  

Null hypothesis is Woman is  pregnant

The test shows woman is pregnant but the doctor mismatch test charts and declares that woman is not pragnent that means the claim , the woman not pregnant prevails

This is the case of Type I error as null hypothesis is rejected when it is true .

2. Husband is pregnant

Null hypothesis is Husband is not pregnant

The test shows husband is pregnant but the doctor mismatch test charts and declares that husband is pragnent that means the claim , the husband is pregnant prevails

This is the case of Type II error as it fails to reject null hypothesis  when it is true .