Question

Q3. The student was interested in her success at basketball free throws. This study investigated whether there was any relationship between the quantitative variable "number of shots 'made' (i.e., successfully completed out of 50 tries)" and two qualitative variables "Time of Day" and "Shoes Worn". The data are here: Made Time Morning Morning Night Night Morning Morning Night Night Morning Morning Night Night Morning Morning Night Night Shoes Others Others 25 26 2 OtherS 27 Others Favorite Favorite 32 Favorite Favorite 30 Others Others 35 4 Others Others 30 Favorite Favorite 37 36 Favorite Favorite

Answer 1

a)

The model for ANOVA is

$y_{i,j}=\mu +\alpha _{i}+\beta _{j}+\gamma _{ij}+e_{ij}$

i=1,2............ j=1,2

b)

Individual 95% CIs For Mean Based on Pooled StDev shoe Mean 1 29.625 32.750 27.0 30.0 33.0 36.0 Individual 95% CIs For Mean Based on Pooled StDev time Mean 1 30.500 2 31.875 27.5 30.0 32.5 35.0

The mean of shoe and time is above.

c) for the ANOVA table we have run this problem in MINITAB as below

Two-way ANOVA: y versus time, shoe MS F Source time shoe Interaction Error Total DF 1 7.563 7.5625 0.34 0.568 1 39.063 39.0625 1.78 0.207 18.063 18.0625 0.82 0.382 12 263.750 21.9792 15 328.438 S: 4.688 R-Sq 19.70% R-Sq ( adj ) -0.00% -

The filled ? in the table as above.

d)

in the model we got all p-values > 0.05. Hence we can claim that the model is not significant at any of the factors. that is by model A and model B and interaction is not significant at 95% confidence.

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