Statistics

[Use R] The cost of auto insurance varies by coverage, location, and the driving record of the driver. The goal of the experiment described here is to compare the average annual insurance cost for five insurance companies (A, B, C, D, E). Four cities of different sizes were selected. The following are estimates of the annual cost for standard coverage for five young male drivers residing in each of the four cities (20 males in total), with no accidents or violations, driving new 2021 Toyota Highlanders:
Insurance company
City 
A 
B 
C 
D 
E 
Pella 
1572 
1108 
1507 
767 
1460 
Waterloo 
1492 
1300 
1646 
931 
1568 
Des Moines 
1447 
1156 
1844 
1063 
1914 
Sheldon 
1393 
1110 
1449 
727 
1686 

What design was used in this experiment? _____________________

Construct the ANOVA table for this experiment. Copy/paste (or write) it here:

At a 5% significance level, do we have enough evidence to conclude that there is a difference in mean annual cost between the different insurance companies? YES NO Write down the pvalue used to answer this question _______

Use Tukey’s method to conduct pairwise comparisons of mean costs for these insurance companies. Copy/paste the output below. Which companies have the same mean annual cost of insurance? ________________________________________________

An experiment was conducted to determine if there is a difference in mean rating between four smartphone suppliers (labeled 14). Four smartphones were ordered from each supplier and each smartphone was rated on the scale 0100. The following ANOVA table was obtained:
Df Sum Sq Mean Sq F value
supplier 3 246.1 82.05 5.831
Residuals 12 168.8 14.07

What are the treatments in this experiment? __________

At a significance level of 0.05, write down the rejection region of the test that compares the treatment means ____________. Is there enough evidence to conclude that there is a difference in mean rating between these suppliers? YES NO

The (sample) mean rating of each supplier is listed below:
Supplier 1 2 3 4
67.850 67.525 62.650 58.300
Use Fisher’s LSD method to perform pairwise comparisons of mean ratings between suppliers. The LSD value is _________

The following ANOVA table was obtained for an RCBD, where the treatments are several bonding agents:
Df Sum Sq Mean Sq F value Pr(>F)
agent 3 24.52 8.17 0.510 0.6855
batch 3 246.14 82.05 5.116 0.0245 *
Residuals 9 144.33 16.04

How many bonding agents were used in this experiment? _______

If the batches have random effects and the treatments have fixed effects, what percent of the total variability of the response variable is due to the different batches? _______
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