Fill in the following for a possible study with one independent variable (IV) wi

Question

Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio):

Independent variable = ______________

Condition A = ______________

Condition B = ______________

Dependent variable = _______________

How do you know this DV is measured on a continuous scale? Now, how would you word the null hypothesis for your sample study? How would you word the alternative hypothesis for your sample study? What alpha level would you set to test your hypothesis? Why

Explanation / Answer

Solution :-

Independent variable = education level
Condition A = higher education level leads to higher income
Condition B = higher education level does not lead to higher income
Dependent variable = higher income

Dependent variables are measured on continuous scale as we know that if a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.

For examples (this will clarify the difference between discrete and continuous variables)

Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.

Similarily, Income can take any value from lower to the hight value.

Hypothesis

The null hypothesis reflects that there will be no observed effect for our experiment. In a mathematical formulation of the null hypothesis there will typically be an equal sign. This hypothesis is denoted by H0.

The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.

If the null hypothesis is not rejected, then we must be careful to say what this means.

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either Ha or by H1.

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis.

State the Hypothesis-

Null hypothesis - Ho ; Higher education leads to higher income

Alternate hypothesis - Ha; Higher education does not lead to higher income

The significance level is used to judge whether the test results are statistically significant. The significance level also determines the probability of error that is inherent in the test.

If the probability that an event occurs is less than , the usual interpretation is that the event did not occur by chance. Formally, is the maximum acceptable level of risk for rejecting a true null hypothesis (Type I error) and is expressed as a probability ranging between 0 and 1. The smaller the significance level, the less likely you are to make a Type I error, and the more likely you are to make a Type II error. Therefore, you should choose an alpha that balances these opposing risks of error based on their practical consequences in your specific situation.

Usually, a significance level (denoted as or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

We choose a larger alpha, such as 0.10, to be more certain that you will not miss detecting a difference that might exist.Therefore, we choose an of 0.1 to be more certain that we will detect any possible difference in the stability.

When to choose a smaller alpha

Choose a smaller alpha, such as 0.01, to be more certain that you will only detect a difference that really does exist.

Here, we can select a significance level of 0.05 which indicates a 5% risk of concluding that a difference exists when there is no actual difference.

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