A psychologist theorized that people can hear better when they have just eaten a large meal. Six individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. The hearing ability scores (high numbers indicate greater ability) are given in the following table. Using the .05 level, do the results support the psychologist’s theory?

 

48. What kind of hypothesis test will you use to analyze this dataset?

Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.

The students receive the following arithmetic test scores:

1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?

(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.

(b) The population mean test scores for all three treatments are equal.

(c) The population mean test scores for all three treatments are different.

(d) The population mean test scores for all three treatments are not all equal.

2.) Calculate the degrees of freedom and the variances for the following ANOVA table:

The formula for the F-ratio is:

3.) Using words, the formula of the F-ratio can be written as:

4.) Using the data from the ANOVA table given, the F-ratio can be written as:

5.) Calculate for F-ratio:

6.) At the level of significance, what is your conclusion?

(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.

(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(d)You can reject the null hypothesis; caffeine does appear to affect test performance.

The following table depicts the four possible outcomes of a hypothesis test: The researcher makes a correct decision (either by correctly rejecting the null hypothesis or correctly not rejecting the null hypothesis), makes a Type I error, or makes a Type II error. In each of the following boxes, select the description that matches the outcome.

The probability of a Type I error is ......, and the probability of a Type II error is.

 Possible outcomes of a hypothesis test:

The following table depicts the four possible outcomes of a hypothesis test: The researcher makes a correct decision ther by correctly rejecting the null hypothesis or correctly not rejecting the null hypothesis, makes a Type I or, or makes a Type II error. In each of the following boxes, select the description that matches the outcome.

The probability of a Type I error is , and the probability of a Type II error is.........

1.) Which of the following answers represents the objective of a hypothesis test?

a. Rejecting the null hypothesis when it is true.

b. Rejecting the null hypothesis when it is false.

c. Not rejecting the null hypothesis when it is true.

d. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.

2.) If the chosen significance level is ? = 0.05, then

a. there is a 5% probability of rejecting a true null hypothesis

b. there is a 5% probability of accepting a true null hypothesis

c. there is a 5% probability of rejecting a false null hypothesis

d. there is a 5% probability of accepting a false null hypothesis