# Hypothesis Testing

• thedeath
In summary, the test that will be performed on the given question is a hypothesis test for the mean of hours devoted to patient care per week by doctors, using either conventional or alternative methods. The test will be conducted at the 10% level of significance and can potentially be a two-sided Z-test or one-sided Z-test if the standard deviation is known, or a two-sided t-test or one-sided t-test if the standard deviation is unknown. Additionally, a one-sided Z-test can also be performed for the proportion of practitioners using conventional methods.
thedeath
Need to know the test that will be performed on the following question:

The data comprises hours devoted to patient care per week for practitioners in conventional and alternative medical practices.

Question:
Can we infer that the mean amount of time devoted to patient care per week by doctors using conventional methods exceeds that of doctors using alternative methods? Test at the 10% level of significance.

What test will be performed:
Hypothesis Test for m (s known)--Two-sided Z-Test
Hypothesis Test for m (s known)--One-sided Z-Test
Hypothesis Test for m (s unknown)--Two-sided t-Test
Hypothesis Test for m (s unknown)--One-sided t-Test
Hypothesis Test for p--One-sided Z-Test

This is plainly a theory question, to test your knowledge of the theory. You should therefore refer to your reading materials and try to gain a good understanding of the subject.

If you short-cut through the theory, that will probably hurt you in the end.

The appropriate test to be performed for this question would be a Hypothesis Test for m (s unknown)--Two-sided t-Test. This is because we are comparing the means of two independent samples (doctors using conventional methods and doctors using alternative methods) and the standard deviation for the population is unknown. We also have a specific hypothesis that the mean for conventional doctors is greater than the mean for alternative doctors, making it a two-sided test. The significance level of 10% means that we will reject the null hypothesis if the p-value is less than 0.10.

## 1. What is the purpose of hypothesis testing?

Hypothesis testing is used to determine whether a particular hypothesis about a population is supported by the available evidence. It allows scientists to make conclusions and predictions about a population based on a sample of data.

## 2. What are the steps of hypothesis testing?

The steps of hypothesis testing include: 1) stating the null and alternative hypothesis, 2) determining the appropriate test statistic and its distribution, 3) collecting and analyzing data, 4) calculating the p-value, and 5) making a decision about the null hypothesis based on the p-value.

## 3. What is a null hypothesis?

A null hypothesis is a statement that assumes there is no significant difference or relationship between variables being studied. It is typically denoted as H0 and is the starting point for hypothesis testing.

## 4. How do you determine the significance level for hypothesis testing?

The significance level, also known as alpha, is typically set at 0.05 or 0.01. This represents the probability of rejecting the null hypothesis when it is actually true. The significance level is chosen by the researcher based on the desired balance between making a correct decision and avoiding a Type I error (incorrectly rejecting the null hypothesis).

## 5. What is a p-value and how is it used in hypothesis testing?

The p-value is the probability of obtaining results at least as extreme as the observed results if the null hypothesis is true. It is compared to the significance level to determine whether the null hypothesis should be rejected or not. A p-value less than or equal to the significance level indicates that the results are statistically significant and the null hypothesis can be rejected.

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