PS214 exam 2

Briefly explain the difference between a Type I error and a Type II error.

A researcher commits a Type I error when they reject a null hypothesis that is actually true. In contrast, they commit a Type II error when they retain a null hypothesis that is actually false.

Draw a conclusion for a two-tailed test at the .05 significance level. Explain what this conclusion means.

Because the observed value of t (df) falls between - ___ and +___, we retain the null hypothesis. The two sample means are not significantly different from each other. (This means we do not have strong evidence that, on average, consuming corn syrup vs. cane sugar leads rats to weigh different amounts.)

Briefly explain the role of critical values and rejection regions in hypothesis testing.

Critical values and rejection regions help a researcher determine whether their observed data provide strong enough evidence against the null hypothesis that they should reject it. Specifically, if their test statistic falls in a rejection region, then they should reject the null hypothesis in favor of the alternative hypothesis. Otherwise, they should retain the null hypothesis. Critical values separate the rejection region(s) from the rest of the test statistic's sampling distribution.

Write a short paragraph that draws a conclusion in terms of the key statistical question and hypotheses

On average, participants who ___ engaged in more ___ (M = ___ ) than did people in the control group (M =___), but this difference was not statistically significant (t = ___, p > .05). This result doe snot provide strong evidence that ___ affects ___ in everyday life.

What does it mean for a researcher to set the significance level (α) for a hypothesis test at .01?

Setting the significance level at .01 means that the researcher will reject the null hypothesis only if there would be less than a 1% chance, if the null hypothesis were actually true, of obtaining the observed data.

If a researcher sets the significance level (α) for a hypothesis test at .05, what does this mean in terms of the probability that they will draw an incorrect conclusion (i.e., commit an error)? Make sure to note what type of error that would be.

Setting the significance level at .05 means that, if the null hypothesis is actually true, then the researcher has a 5% chance of incorrectly rejecting it (i.e., committing a Type I error).

If the statistical power for a study is .85, what does this mean in terms of the probability that the researcher will draw an incorrect conclusion (i.e., commit an error)? Make sure to note what type of error that would be.

Statistical power of .85 means that, if the null hypothesis is actually false, then the researcher has a 15% chance of incorrectly retaining it (i.e., committing a Type II error).

What would the critical value(s) and rejection region(s) be for a two-tailed test at the .05 significance level?

The critical values would be +/- _____ We would reject the null hypothesis if t were greater than +___ or less than -___. We would retain the null hypothesis if t were between -___ and +___

Why they should conduct a matched-samples t-test?

They should conduct a matched-samples t-test, because (a) they want to test whether two means differ from each other, and (b) there's a good reason why each score in the ___ sample should be paired with a particular score from the ___ sample: (each pair of scores comes from the same participant.)

why they should conduct a one-sample t-test

They should conduct a one-sample t-test, because (a) they want to test whether a single population mean (for ___ ) differs from a particular value (___), and (b) they don't know the population standard deviation.

why they should conduct a z-test

They should conduct a z-test, because (a) they want to test whether a single population mean (for ___) differs from a particular value (___), and (b) they know the population standard deviation ( ___ ).

why they should conduct an independent samples t-test

They should conduct an independent-samples t-test, because (a) they want to test whether two population means differ from each other, and (b) there's no reason why each___ in the ___ group should be paired with a particular____ in the _______ group.

Explain what this confidence interval means, and how it relates to the conclusion that you drew in part f.

This confidence interval means we can be ___% confident that the true population mean for only children falls between ___ and ___. Whenever the ___% confidence interval does not include the value of μ0—as in this case, where μ0 = 50—it means that conducting a two-tailed test at the .05 significance level (as in part f) will lead us to reject the null hypothesis.

Compute Cohen's d. Briefly explain what this value indicates

This indicates that the average ___ of the participants who ___ was 0.33 standard deviation units greater/less than the average ___ of the participants who ___. This represents a ___ effect of ___ on ___.

Summarize your findings in one brief paragraph (for a z test)

We conducted a two-tailed z test to examine whether ___ have higher ___ than ___. The sample mean of ___ was significantly different than the population average of___ (z = ___, p < .05). This result provides strong evidence that ___ have higher ___ `than the general population.