Problem 2 b) Compute the 95% confidence intervals for 60 and B1- c) Perform a hy

Question

Problem 2

b) Compute the 95% confidence intervals for 60 and B1- c) Perform a hypothesis test to see if the slope is greater than -0.6 2. A study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each four temperatures, and the compressive strength of ead specimen is measured (in Mpa). The results are as follows Strengths 31.2 29.6 30.8 30.0 31.4 30.0 27.7 31.1 31.3 30.6 35.9 36.8 35.0 34.6 36.5 38.3 37.0 37.5 36.1 38.4 Temperature (oc) 10 20 30 a) Construct an ANOVA table b) Can you conclude that the mean strength differs with temperature? 3. Fill in the missing numbers in the One-Way ANOVA table Sign In | MasteringEngin Source of Variation Degrees of Freedom Sum of Squares Mean SquareF 176.482(a) Between Treatment Error Total 19 235.958

Explanation / Answer

Q2.

Step 1

null, Ho: µ1 =µ2 =µ3 =µ4

alternative, H1: atleast one mean is diffrent to each other

Step 2

Degrees of freedom between = k - 1 = 4 - 1 = 3

Degrees of freedom Within = n - k = 20 - 4 = 16

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.239

Step 3

Grand Mean = G / N = 30.6+30.14+35.76+30.24 / 4 = 31.685

SST = ( Xi - GrandMean)^2 = (31.2-31.685)^2 + (29.6-31.685)^2 + (30.8-31.685)^2 + ……..& so on = 266.186

SS Within = (Xi - Mean of Xi ) ^2 =,(31.2-30.6)^2 + (29.6-30.6)^2 + (30.8-30.6)^2 + ……..& so on = 244.378

SS Between = SST - SS Within = 266.186 - 244.378 = 21.808

Step 4

Mean Square Between = SS Between / df Between = 21.808/3 = 7.269

Mean Square Within = SS Within / df Within = 244.378/16 = 15.274

Step 5

F Cal = MS Between / Ms Within = 7.269/15.274 = 0.476

We got |F cal| = 0.476 & |F Crit| =3.239

MAKE DECISION

Hence Value of |F cal| < |F Crit|and Here We Accept Ho

b. mean rate is similar between them

Treatments ONE WAY ANOVA Mean = X /n 0 31.2 29.6 30.8 30 31.4 30.6 10 30 27.7 31.1 31.3 30.6 30.14 20 35.9 36.8 35 34.6 36.5 35.76 30 38.3 37 37.5 36.1. 38.4 30.24

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