5. (5 pts) An investigative study collected 150 sample of observations from the

Question

5. (5 pts) An investigative study collected 150 sample of observations from the river Wabash, at random locations near Lafayette. Each observation consisted of a measure of water pH (X) and fish count (Y). The researchers are interested in how the acidity of the water affects the number of fish. Complete the following ANOVA table for the regression analysis. State the null and alternative hypotheses for the F-test as well as your conclusion in sentence form. You may use the critical F (critical t) approach or the p-value approach. Statistics 512 Homework 1 Due Monday, Jun 18 2018 MS 46.7 Degrees of freedom |SS F-value Source Model Error Total 83.7

Explanation / Answer

null hypothesis: Ho: theere is no regression between measure of water and fish count.

alternate hypothesis":Ha: theere is a signifcant regression between measure of water and fish count.

df(model)=number of independent variable =p=1

df(error)=n-p-1=150-1-1=148

as SS(model)=MS(model)*df(model)

and MS(error)=SS(error)/df(error)

also F =MS(model)/MS(error)

from above:

for (1,148) degree of freedom and 0.05 level ; critical value F=3.91

as test statistic 26.41 is higher than crifical value ; we reject null hypotheiss

we have sufficient evidence to conclude that   there is a signifcant regression between measure of water and fish count.

source df SS MS F model 1 46.7 46.7 26.41 error 148 83.7 1.77 total 149

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