What is a null and alternatives hypothesis.
Give two example each on a P value
In statistics, a null hypothesis (H0) is a statement that assumes there is no significant difference or relationship between variables. It is the hypothesis that researchers aim to disprove or reject. On the other hand, an alternative hypothesis (Ha or H1) is a statement that contradicts the null hypothesis and suggests a significant difference or relationship between variables.
Examples of null and alternative hypotheses:
1. Null hypothesis: There is no difference in the mean heights of men and women.
Alternative hypothesis: There is a significant difference in the mean heights of men and women.
2. Null hypothesis: There is no association between smoking and lung cancer.
Alternative hypothesis: There is a significant association between smoking and lung cancer.
The P value is a statistical measure used to determine the strength of evidence against the null hypothesis. It represents the probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true. A low P value suggests strong evidence against the null hypothesis, whereas a high P value indicates weak evidence.
Examples of P values:
1. P value = 0.036: In a study comparing two groups, a P value of 0.036 indicates that there is a 3.6% chance of obtaining the observed difference between groups if the null hypothesis is true. This value suggests that there is evidence against the null hypothesis and suggests a significant difference between groups.
2. P value = 0.218: In a study investigating the correlation between two variables, a P value of 0.218 indicates that there is a 21.8% chance of obtaining the observed correlation coefficient if the null hypothesis of no correlation is true. This value suggests weak evidence against the null hypothesis and indicates that there is no significant correlation between the variables.
A null hypothesis is a statement that assumes there is no difference or relationship between variables in a population. It is typically written as H0. An alternative hypothesis, on the other hand, suggests that there is a difference or relationship between variables. It is denoted as Ha or H1.
Example 1:
Null hypothesis (H0): There is no difference in mean test scores between students who received tutoring and those who did not.
Alternative hypothesis (Ha): There is a difference in mean test scores between students who received tutoring and those who did not.
Example 2:
Null hypothesis (H0): There is no correlation between hours of study and exam grades.
Alternative hypothesis (Ha): There is a correlation between hours of study and exam grades.
Now, let's explain two examples of P-values:
Example 1:
P-value = 0.03
In this example, if the null hypothesis were true, there would only be a 3% chance of observing the observed effect (or more extreme) due to random chance alone.
Example 2:
P-value = 0.50
In this example, if the null hypothesis were true, there would be a 50% chance of observing the observed effect (or more extreme) due to random chance alone. This high P-value suggests that we do not have enough evidence to reject the null hypothesis.
A null hypothesis is a statement that assumes there is no significant difference or relationship between variables in a population. It represents the status quo or the absence of an effect. An alternative hypothesis is a statement that contradicts or negates the null hypothesis, proposing that there is a significant difference or relationship between variables.
Example 1:
Null hypothesis (H0): There is no difference in mean test scores between students who study for 2 hours and students who study for 4 hours.
Alternative hypothesis (H1): There is a significant difference in mean test scores between students who study for 2 hours and students who study for 4 hours.
Example 2:
Null hypothesis (H0): The usage of a new drug does not affect the recovery time of patients.
Alternative hypothesis (H1): The usage of a new drug significantly reduces the recovery time of patients.
P-value is a statistical measure used to determine the strength of evidence against the null hypothesis. It represents the probability of finding the observed results (or more extreme results) if the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis.
Example of a small P-value: Let's say a study calculates a P-value of 0.02. This means that if the null hypothesis is true, there is only a 2% chance of observing the obtained results or more extreme results.
Example of a large P-value: If the calculated P-value is 0.47, it means that if the null hypothesis is true, there is a 47% chance of observing the obtained results or more extreme results, which is not statistically significant.