5.12 Comparing fonts. Suppose that an instructor wants to investigate whether th

Question

5.12 Comparing fonts. Suppose that an instructor wants to investigate whether the font on an exam affects student performance as measured by the final exam score. She uses four differ fonts (times, courier, helvetica, comic sans) and randomly assigns her 40 students to one of those used four fonts. a. Identify the explanatory and response variables in this study b. Is this an observational study or a randomized experiment c. Even though the subjects in this study were not randomly selected from a population, it's ? Explain how you know. still appropriate to conduct an analysis of variance. Explain wlhy. 5.13 Comparing fonts (continued). Refer to Exercise 5.12. Determine each of the entries that would appear in the "degrees of freedom" column of the ANOVA table. 5.14 All false. Reconsider the previous exercise. Now suppose that the p-value from the ANOVA F-test turns out to be 0.003. All of the following statements are false. Explain why each one is false. a. The probability is 0.003 that the four groups have the same mean score. b. The data provide very strong evidence that all four fonts produce different mean scores. c. The data provide very strong evidence that the comic sans font produces a different mean score than the other fonts. d. The data provide very little evidence that at least one of these fonts produces a different mean score than the others. e. The data do not allow for drawing a cause-and-effect conclusion between font and exam score. f. Conclusions from this analysis can be generalized to the population of all students at the instructor's school.

Explanation / Answer

dear student please post the question one at a time:

a) Explanatory Variables vs. Response Variables. Theresponse variable is the focus of a question in a study or experiment. An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable.

Response variable here is the final score

Explanatory variable here is the fonts (four different fonts)

b) randomization involves randomly allocating the experimental units across the treatment groups.

An observational study is a study in which the researcher simply observes the subjects without interfering. That is, the researcher has no control over any treatments the subjects may be given or which groups the subjects may be separated into, etc. They just observe the subjects and record data based on their observations.

Hence this is a randomized experiment as we are randomly allocating 40 students to 4 fonts groups.

c)The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

We have four different fonts and we are compairing the mean final score of the students in these four groups, hence we will use analysis of variance.

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