An experiment on mung beans was performed to investigate the environmental effects of salinity and water temperature on sprouting. Forty beans were randomly allocated to each of 36 petri dishes that were subject to one of four levels of Salinity (0, 4, 8, and 12 ppm) and one of three Temperatures (32°, 34°, or 36° C). After 48 hours, the biomass of the sprouts was measured.
Here are partial box plots of Biomass on Salinity and Temperature:

The interaction plot shows

A two-way ANOVA model is fit, and the following ANOVA table results:

The plot of residuals vs. predicted values shows:

a) State the hypotheses about the factors (both numerically and in words).
b) Are the conditions for two-way ANOVA met?
c) Perform the hypothesis tests and state your conclusions. Be sure to state your conclusions in terms of biomass, salinity, and water temperature.

Transcribed Image Text:

E 10.00 8.75 7.50 10 32 34 35 Temperature (C) 0 4 8 12 Salinity (ppm) 10 Salinity (ppm) 12 32 34 36 Temperature (c) Analysis of Variance for Biomass (g) Sum of Mean DF Squares Square F-ratio P-value 3 36.4701 12.1567 16.981 <0.0001 2 34.7168 17.3584 24.247 <0.0001 Source Salinity Temp Salinity X Temp 6 5.2972 0.8829 1.233 0.3244 Error Total 24 17.1816 0.7159 35 93.6656 0.75 キ++ 10 Predicted Values (g)