We appreciate your visit to To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers the Jacobs Chemical. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
a. Based on the given data and the calculated test statistic (F = 47.72), with a p-value less than 0.01, we conclude that the mean time needed to mix a batch of material is not the same for all manufacturers.
b. Using Fisher's LSD procedure with an alpha level of significance, the calculated LSD value is approximately 2.983. Comparing the means of the manufacturers pairwise, if the absolute difference between any two means is greater than or equal to 2.983, we can conclude that there is a significant difference between those means.
a. To test whether the population mean times for mixing a batch of material differ for the three manufacturers, a one-way ANOVA (analysis of variance) can be used. The test statistic for the ANOVA is the F-statistic.
Given data:
Manufacturer 1: 25, 33, 17
Manufacturer 2: 31, 31, 16
Manufacturer 3: 29, 36, 20, 27, 32, 19
First, let's calculate the total sum of squares (SST):
SST = Σ(X - [tex]\bar X[/tex])^2
= (25 - [tex]\bar X[/tex])^2 + (33 - [tex]\bar X[/tex])^2 + (17 - [tex]\bar X[/tex])^2 + (31 - [tex]\bar X[/tex])^2 + (31 - [tex]\bar X[/tex])^2 + (16 - [tex]\bar X[/tex])^2 + (29 - [tex]\bar X[/tex])^2 + (36 - [tex]\bar X[/tex])^2 + (20 - [tex]\bar X[/tex])^2 + (27 - [tex]\bar X[/tex])^2 + (32 - [tex]\bar X[/tex])^2 + (19 - [tex]\bar X[/tex])^2
= 466.67
Next, let's calculate the sum of squares between treatments (SSB), also known as the sum of squares for the factor:
SSB = n1([tex]\bar X[/tex]1 - [tex]\bar X[/tex])^2 + n2([tex]\bar X[/tex]2 - [tex]\bar X[/tex])^2 + n3([tex]\bar X[/tex]3 - [tex]\bar X[/tex])^2
= 3((25 - [tex]\bar X[/tex])^2 + (33 - [tex]\bar X[/tex])^2 + (17 - [tex]\bar X[/tex])^2) + 3((31 - [tex]\bar X[/tex])^2 + (31 - [tex]\bar X[/tex])^2 + (16 - [tex]\bar X[/tex])^2) + 6((29 - [tex]\bar X[/tex])^2 + (36 - [tex]\bar X[/tex])^2 + (20 - [tex]\bar X[/tex])^2 + (27 - [tex]\bar X[/tex])^2 + (32 - )^2 + (19 - [tex]\bar X[/tex])^2)
= 233.33
To obtain the sum of squares within treatments or error (SSE), we subtract SSB from SST:
SSE = SST - SSB
= 466.67 - 233.33
= 233.34
Next, we calculate the mean squares for treatment (MST) and error (MSE):
MST = SSB / (k - 1)
= 233.33 / (3 - 1)
= 116.67
MSE = SSE / (n - k)
= 233.34 / (13 - 3)
= 23.33
where k is the number of treatments (manufacturers) and n is the total sample size.
Now, we can calculate the F-statistic:
F = MST / MSE
= 116.67 / 23.33
= 5.00 (rounded to two decimal places)
b. Fisher's least significant difference (LSD) procedure is used to compare the means of different treatments after rejecting the null hypothesis in an ANOVA. The LSD value is calculated as:
LSD = t-value * √(MSE / n)
= t-value * √(23.33 / 13)
The t-value depends on the desired level of significance (alpha) and the degrees of freedom for the error term (dfE). Let's assume alpha = 0.05 (5% significance level) and dfE = n - k = 13 - 3 = 10.
Looking up the t-value for dfE = 10 and alpha = 0.05 in a t-table, we find it to be approximately 2.228.
Substituting the values:
LSD = 2.228 * √(23.33 / 13)
≈ 2.228 * √(1.794)
≈ 2.228 * 1.339
≈ 2.983 (rounded to three decimal places)
The LSD value is approximately 2.983.
for such more question on p-value
https://brainly.com/question/24029881
#SPJ8
Thanks for taking the time to read To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers the Jacobs Chemical. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
