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Jimmy Kimmel Live! on ABC, The Tonight Show Starring Jimmy Fallon on NBC, and The Late Show with Stephen Colbert on CBS are three popular late-night talk shows. The following table shows the number of viewers in millions for a 10 -week period during the spring for each of these shows (TV by the Numbers website).

$\begin{aligned} &\text { The Tonight Show }\\ &\begin{array}{lccc} \text { Week } & \begin{array}{c} \text { Jimmy Kimmel } \\ \text { Live (ABC) } \end{array} & \begin{array}{c} \text { Starring Jimmy } \\ \text { Fallon (NBC) } \end{array} & \begin{array}{c} \text { The Late Show with } \\ \text { Stephen Colbert (CBS) } \end{array} \\ \text { June 13-June 17 } & 2.67 & 3.24 & 2.27 \\ \text { June 6-June 10 } & 2.58 & 3.32 & 2.05 \\ \text { May 30-June 3 } & 2.64 & 2.66 & 2.08 \\ \text { May 23-May 27 } & 2.47 & 3.30 & 2.07 \\ \text { May 16-May 20 } & 1.97 & 3.10 & 2.31 \\ \text { May 9-May 16 } & 2.21 & 3.31 & 2.45 \\ \text { May 2-May 6 } & 2.12 & 3.20 & 2.57 \\ \text { April 25-April 29 } & 2.24 & 3.15 & 2.45 \\ \text { April 18-April 22 } & 2.10 & 2.77 & 2.56 \\ \text { April 11-April 15 } & 2.21 & 3.24 & 2.16 \end{array} \end{aligned}$

At the .05 level of significance, test for a difference in the mean number of viewers per week for the three late-night talk shows.

Solution

VerifiedIn this item, we are to conduct a test to determine whether there is a difference in the mean number of viewers per week for the three shows.

To do so, we check for any significant difference in the mean number of viewers using Analysis of Variance (ANOVA), where we are told to use $\alpha=0.05$ as our level of significance.

We are then given data for the mean weekly viewers for 10 weeks across the three shows. We will then consider the given data as a Randomized Block Design and try to remove the block effects.

*Why do we consider the data as a Randomized Block Design and what variable do we consider as the blocks?*

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