For each of the following situations, determine:

a) the null and research hypotheses;
b) the hypothesis test used (normal curve, single sample t-test, dependent samples t-test, independent samples t-test, ANOVA). For situations 1, 3, 4, and 5, also state whether the test is unilateral or bilateral;
c) the degrees of freedom
d) the critical value (cutoff score on the comparison distribution);
e) your sample’s test score;
f) your conclusion on whether to accept or reject the null hypothesis (you must show how the comparison of your cutoff score with your sample’s test score leads to your conclusion).

For each situation, assume that any information that is not provided is therefore unknown to the researcher. Also, assume that the level of significance (alpha) is 0.05.

1. A researcher wants to determine whether alcohol increases the amount of motor coordination errors. She selects two samples of 25 participants each. One group receives 5 ounces of alcohol, while the other group receives 5 ounces of water. She then observes the amount of errors that the participants make in a labyrinth. The test statistic was 2.81.

2. The same researcher wants to study the effect of caffeine on memory. She selects four samples of 15 participants each. The groups receive 0, 2, 4, and 6 cups of coffee, respectively. The researcher takes note of the amount of words that the participants remember after studying them for 20 seconds. The test statistic was 3.15.

a) The null and research hypotheses for situation 1 are as follows:

Null hypothesis (H0): Alcohol does not increase the amount of motor coordination errors.
Research hypothesis (Ha): Alcohol increases the amount of motor coordination errors.

The null and research hypotheses for situation 2 are as follows:

Null hypothesis (H0): Caffeine does not affect memory.
Research hypothesis (Ha): Caffeine affects memory.

b) For situation 1, the appropriate hypothesis test to use is an independent samples t-test, as there are two independent groups being compared.

For situation 2, the appropriate hypothesis test to use is an ANOVA (Analysis of Variance), as there are four independent groups being compared.

c) The degrees of freedom for an independent samples t-test are calculated based on the sample sizes of the two groups. In this case, since both groups have 25 participants each, the degrees of freedom would be (25 - 1) + (25 - 1) = 48.

The degrees of freedom for an ANOVA are calculated differently. It is based on the number of groups being compared and the total sample size. In this case, there are four groups with 15 participants each, so the degrees of freedom would be (4 - 1) = 3.

d) The critical value (cutoff score on the comparison distribution) can be obtained from a t-table for an independent samples t-test and from an F-table for an ANOVA test. Since the level of significance is 0.05, the critical value for both tests would be the value that corresponds to a 95% confidence level.

e) The sample's test score, given in the question, is 2.81 for situation 1 and 3.15 for situation 2.

f) To determine whether to accept or reject the null hypothesis, we compare the sample's test score with the critical value. If the sample's test score falls in the critical region (i.e., it is greater than or less than the critical value), we reject the null hypothesis. If the sample's test score falls outside the critical region, we fail to reject the null hypothesis.

For situation 1, since the test is unilateral (we are testing whether alcohol increases motor coordination errors), we would look for the critical value of the t-distribution with 48 degrees of freedom in the appropriate tail (either the upper tail or lower tail, depending on the specific direction of the research hypothesis). If the sample's test score is greater than the critical value, we reject the null hypothesis.

For situation 2, since it is an ANOVA test, we compare the test statistic (3.15) with the critical value obtained from the F-table using the appropriate degrees of freedom. If the test statistic is greater than the critical value, we reject the null hypothesis.

Note: The critical value and specific conclusion cannot be determined without the significance value (alpha) and the directions of the research hypotheses in both situations.