What is a null and alternatives hypothesis.
Give two example each in a p value of 0.05
A null hypothesis is a statement that suggests there is no statistical relationship or difference between two variables in a population. It is typically denoted as H₀.
An alternative hypothesis, on the other hand, is a statement that contradicts or negates the null hypothesis. It suggests that there is indeed a statistical relationship or difference between the variables being studied. It is denoted as H₁ or Hₐ.
Example 1:
Null hypothesis (H₀): There is no significant 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): There is no significant correlation between age and cholesterol levels in the population.
Alternative hypothesis (H₁): There is a significant correlation between age and cholesterol levels in the population.
In both examples, a p-value of 0.05 is chosen as the threshold. A p-value of 0.05 means that if the observed data's probability of occurring under the null hypothesis is 5% or less, then the null hypothesis will be rejected in favor of the alternative hypothesis.
A null hypothesis is a statement that suggests there is no significant difference or relationship between variables in a population. It is usually denoted by H0.
An alternative hypothesis, on the other hand, is a statement that suggests there is a significant difference or relationship between variables in a population. It is denoted by H1 or Ha.
Examples of null and alternative hypotheses with a p-value of 0.05 could be:
Example 1:
Null hypothesis: There is no significant difference in the average test scores of students who study for 1 hour and students who study for 2 hours.
Alternative hypothesis: There is a significant difference in the average test scores of students who study for 1 hour and students who study for 2 hours.
Example 2:
Null hypothesis: There is no significant effect of a new drug on reducing blood pressure.
Alternative hypothesis: There is a significant effect of a new drug on reducing blood pressure.
Please note that the selection and formulation of null and alternative hypotheses are specific to the research question and may vary depending on the context and variables being studied.
A null hypothesis (H0) is a statement that assumes there is no statistical relationship or significant difference between two variables in a population. It is the default hypothesis that assumes no effect, association, or difference between the variables being studied. On the other hand, an alternative hypothesis (H1 or Ha) is a statement that contradicts or challenges the null hypothesis, suggesting that there is a statistically significant relationship or difference between the variables.
When considering a p-value of 0.05, this is a commonly used threshold for statistical significance. It means that if the p-value associated with a statistical test is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis.
Here are two examples each for a null and alternative hypothesis with a p-value of 0.05:
Example 1 - Null Hypothesis:
H0: There is no significant difference in the mean heights of male and female students in a college population.
H0: The average time spent studying does not affect exam scores.
Example 1 - Alternative Hypothesis:
H1: There is a significant difference in the mean heights of male and female students in a college population.
H1: The average time spent studying has a significant effect on exam scores.
Example 2 - Null Hypothesis:
H0: There is no association between smoking and the risk of developing lung cancer.
H0: The type of music played in a store has no effect on customer purchasing behavior.
Example 2 - Alternative Hypothesis:
H1: There is an association between smoking and the risk of developing lung cancer.
H1: The type of music played in a store has a significant effect on customer purchasing behavior.