Could you please explain the answers. Thanks! 8. The moisture i n a wet mix of c

Question

Could you please explain the answers. Thanks!
8. The moisture i n a wet mix of cement was considered to have an effect on the denseness of the finished product. t. The moisture of the mix was controlled at various levels, and the thelow nihed product was measured. The data were entered into SPSS, and the following output was generated 50 52 54 58 5.8 60 Moisture Descriptive Statistics DENSENESS 5.17 MOISTURE 5.30 Mean Std. Deviation N 12 2.52 Model Suummary Adjusted Std. Error of ModelR R SquareR Square the Estimate 729 1.310 ANOVA Sum of Squares Regression 52.500 17.167 Model df Mean Square Si 52500 30.58300025 10 Residual Total Coefficients Unstandardized Standardized Coefficients Beta Coemicients Std. Error 4.81 Model 4.44 00126 (Constan) 21.33 MOISTURE 5.00 Suppose we wish to test if denseness increases with the moisture in the cement mix: Ho: fh = 0 versus H: > 0. Do we reject the null hypothesis at the 1% significance level?Include the value of the t statistic and the corresponding P-value in your answer

Explanation / Answer

From scatterplot we observe

there exists a positive relationship between moisture and denseness

that is as moisture increases ,denseness increases and vice versa.

correlation coefficient=r=-0.868

there exists a positive relationship between mositure and denseness.

R sq=0.754

0.754*100=75.4% variation in denseness is explained by mositure.

Good model.
From Anova table

F=30.583

p=0.00025

model is signiificant.

From Coefficient table,regression eq is

denseness=-21.33+5(mositure)

slope=5

y intercept=-21.33

HO:slope=0

H1:slope>0

alpha=0.01

t=5.53

p=0.0025

p<0.01

reject null hypothesis.

Accept alternative hypothesis.

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