What does it mean when a researcher chooses the cutoff in a comparison distribution to be .01?
a. It means that to reject the null hypothesis, the result must be higher than a z score of .01
b. It means that to reject the null hypothesis there must be less than a 1% chance that the result would have happened by chance if the null hypothesis were true.
c. It means that if the result is larger than .01 (such as .02 or .03), it is statistically significant.
d. It means that the research hypothesis is definitely true if the sample's score on the comparison distribution is less extreme than the cutoff that corresponds to the most extreme .1% of that comparison distribution.
What can be concluded if the null hypothesis is rejected?
a. The research hypothesis is supported
B. The research hypothesis is true and the null hypothesis is false
c. The null hypothesis is true and the research hypothesis is false
d. The null hypothesis should have been based on a directional hypothesis
Suppose a researcher wants to know if there is a gender difference in the number of dreams people remember. The results of such a study would be analyzed using
a. A one-tailed test because only one issue is discussed, dreams
b. A one-tailed test because there is only one interaction, which is between gender and number of dreams
c. A two-tailed test because there is no predicted direction of the difference- the men could remember more or the women could
d. A two-tailed test because there are two variables involved, dreams and gender
When setting up a statistical test, two hypotheses are formed: a null hypothesis and an alternate hypothesis. The null hypothesis tests the probability that the sample mean (taken from sample data) is very likely drawn from the population mean. If there is a low probability that the sample mean has been drawn from the population mean, the null will be rejected and the alternate will be accepted. The significance level (usually stated in a problem) is the probability at which the null will be rejected and the alternate accepted. For example, if a significance level is set at .05, there is a 5% probability that the null will be rejected. Often tables are used for values that correspond to the level stated. These values are known as critical or cutoff values; they cut off the distribution at that point. If an observed value (calculated from a formula) exceeds a critical value from a table, then the null will be rejected. If the observed value does not exceed the critical value from a table, then the null will not be rejected. There are many different kinds of tables depending on the type of test. A one-tailed test shows a difference in a particular direction. A two-tailed test is just looking for a difference in either direction.
I hope these few hints will help you determine your answers.
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The answers to the questions are as follows:
1. What does it mean when a researcher chooses the cutoff in a comparison distribution to be .01?
Answer: b. It means that to reject the null hypothesis there must be less than a 1% chance that the result would have happened by chance if the null hypothesis were true.
2. What can be concluded if the null hypothesis is rejected?
Answer: B. The research hypothesis is true and the null hypothesis is false.
3. Suppose a researcher wants to know if there is a gender difference in the number of dreams people remember. The results of such a study would be analyzed using
Answer: d. A two-tailed test because there are two variables involved, dreams and gender.
For the first question, the correct answer is b. It means that to reject the null hypothesis, there must be less than a 1% chance that the result would have happened by chance if the null hypothesis were true.
To understand why, when conducting hypothesis testing, researchers set a significance level, also known as the alpha level, which represents the maximum acceptable probability of incorrectly rejecting the null hypothesis. In this case, the cutoff in the comparison distribution is set at .01, which means that the researcher is willing to tolerate no more than a 1% chance of making a Type I error (rejecting the null hypothesis when it is true).
Moving on to the second question, when the null hypothesis is rejected, it does not necessarily mean that the research hypothesis is true and the null hypothesis is false. It means that there is enough evidence to suggest that the data provides support for the research hypothesis over the null hypothesis.
Therefore, the correct answer is a. The research hypothesis is supported.
Lastly, for the third question, when analyzing the gender difference in the number of dreams people remember, a two-tailed test would be used because there is no predicted direction of the difference. The number of dreams remembered could be greater in either gender.