Question

The effect of a monetary incentive on performance on a cognitive task was investigated. The researcher predicted that greater monetary incentives would result in higher performance. Participants were told that they would receive either 5 cents, 25 cents, or 50 cents for each word puzzle that they correctly solved. A statistical test showed that there was a significant effect of incentive on performance at the .01 level. The greater the incentive, the more puzzles were solved.
1. What is the null hypothesis?

2. What is the research hypothesis?

3. What would be the Type I error?

4. What would be the Type II error?

5. What is the probability of a Type I error?

Answer 1

Answer:

1) $H_0:\mu_5=\mu_{25}=\mu_{50}$

2) $H_a:\mu_{50}>\mu_{25}>\mu_{5}$

3) A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

4) A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

5) The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.

Step-by-step explanation:

As the claim is that the greater the incentive, the more puzzles were solved, the null hypothesis will state that this claim is not true. That is that there is no significant relation between the incentive and the amount of puzzles that are solved. In other words, the mean amount of puzzles solved for the different incentives is equal (or not significantly different):

$H_0:\mu_5=\mu_{25}=\mu_{50}$

The research (or alternative hypothesis) is that the greater the incentive, the more puzzles were solved. That means that the mean puzzles solved for an incentive of 50 cents is significantly higher than the mean mean puzzles solved for an incentive of 25 cents and this is significantly higher than the mean puzzles solved for an incentive of 5 cents.

$H_a:\mu_{50}>\mu_{25}>\mu_{5}$

A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.