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Problem 1. (Answer the questions that follow the case description) The size of a pizza was measured by 5 students, each using 3 different types of measuring tapes. We would like to know if there is a significant difference among the three measuring tapes. Note: Only one pizza was used for all the measurements, but the pizza was measured three times by each student, once using each measuring tape.

Given the values in the problem, complete the ANOVA table. Enter numeric digits only (whole number), no symbols, units, or text. Round up two decimals if needed.   Source SS df MS F Treatment 480 [dffactor] [F] Error [sse] [dfe] Total 1040 [dftotal]

Problem 3. A tech startup tests 4 keyboard layouts (A, B, C, D) to see which yields faster typing speed (words per minute) for novice users. Thirty‑two (32) volunteers are randomly assigned in a completely randomized design with 8 users per layout, and each user completes one timed trial. The company analyzes the between‑layout variation with a one‑way ANOVA. The total sum of squares and treatment (factor) sum of squares are calculated as follows:  SSTotal = 1040 SSTreatment = 480  

If this experiment is analyzed as a completely randomized design (CRD), what is the error degrees of freedom?  Enter only the numeric value — no units, symbols, or text.  

If a t-test was used to analyze the data, what would be the t-statistic value? 

In a completely randomized design, the sum of squares due to error (SSE) is a measure of the variation in the values of the replicates within a factor level.

If this experiment is analyzed as a randomized complete block design (RCBD), what is the error degrees of freedom?  Enter only the numeric value — no units, symbols, or text.  

The experiment was designed and analyzed as a RCBD (Randomized Complete Block Design) with the following ANOVA results: SS Factor = 60 SS Block = 20 SS Error = 40 If this same experiment were analyzed instead as a completely randomized design (CRD), what would be the total sum of squares for the ANOVA results? Enter only the numeric value — no units, symbols, or text.

For the next two questions, use the following case as context: A popular dietary supplement is being tested for efficacy. Twenty individuals were enlisted as test subjects and each individual was randomly assigned to one of two test groups — the placebo group and the treatment group. Both groups received a pill but only 10 of those were true dietary supplements (the other 10 are placebo pills).  

If the total degrees of freedom in the ANOVA is 23, how many levels does the factor of interest have?