Question

You are planning a completely randomized experiment to investigate the effect on blood pressure from a specific ingredient in a drug. You will use four different amounts for this ingredient (2.5 mL, 5 mL, 7.5 mL, and 10 mL). You randomly select 40 participants to be in the study and then randomly assign 10 participants to each of the four treatments. After two weeks, you record the change in blood pressure for each participant (final blood pressure minus beginning blood pressure).After fitting the one-way ANOVA model, you compute the MSE to be 17. You also compute the sample means for each treatment as ybar_1=115, ybar_2=110, ybar_3=105, ybar_4=120 You would like to perform a test to determine if there is a quadratic trend between the amount of the ingredient in the drug and the change in blood pressure.

          You are planning a completely randomized experiment to investigate the effect on blood pressure from a specific ingredient in a drug. You will use four different amounts for this ingredient (2.5 mL, 5 mL, 7.5 mL, and 10 mL). You randomly select 40 participants to be in the study and then randomly assign 10 participants to each of the four treatments. 
After two weeks, you record the change in blood pressure for each participant (final blood pressure minus beginning blood pressure).After fitting the one-way ANOVA model, you compute the MSE to be 17. You also compute the sample means for each treatment as ybar_1=115, ybar_2=110, ybar_3=105, ybar_4=120
You would like to perform a test to determine if there is a quadratic trend between the amount of the ingredient in the drug and the change in blood pressure.

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Added by Dwayne G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Md.Daniyal Arshad

03/05/2022

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You are planning a completely randomized experiment to investigate the effect on blood pressure from a specific ingredient in a drug. You will use four different amounts for this ingredient (2.5 mL, 5 mL, 7.5 mL, and 10 mL). You randomly select 40 participants to be in the study and then randomly assign 10 participants to each of the four treatments. After two weeks, you record the change in blood pressure for each participant (final blood pressure minus beginning blood pressure).After fitting the one-way ANOVA model, you compute the MSE to be 17. You also compute the sample means for each treatment as ybar_1=115, ybar_2=110, ybar_3=105, ybar_4=120 You would like to perform a test to determine if there is a quadratic trend between the amount of the ingredient in the drug and the change in blood pressure.

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Transcript

00:01 So while seeing the question let's further move to the answer.

00:03 So let's see here that.

00:04 Here is between groups and here is within group and here is total and there is sum of square and there is df and there is mean square.

00:45 So here is difference between groups sum of square is 2 ,267 .6 df is 3 and mean square is 755 .87 and within group sum of squares is 1 ,478 .2 and df is 50 and mean square is 29 .564.

01:16 So total of sum of squares is 3 ,745 .8 and total of df is 53.

01:34 And total of mean square is 785 .44.

01:49 So the first one is hypothesis h -o.

02:10 There is no difference between mean groups, bracket, all mean group is same.

02:41 H .a.

02:42 There is difference between mean group bracket at least one of the group has different mean and the second one is test statistics f is equal to mean square between groups by mean square within group is equal to 755 .87 by 29 .5 .7 .7.

04:28 5664 is equal to 25 by 5667.

04:33 So test status text is 25 .57.

04:46 P value is equal to 0 .00 bracket to get p value use f table or excel command is equal to to f .d .i .s .t.

05:26 Point r .t.

05:28 Bracket 25 .567 .3 .50.

05:47 P value is less than 0 .05.

05:54 Thus we reject.

06:01 Null hypothesis...

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