Question

An article in the material

13-12. An article in the Materials Research Bulletin (1991, Vol. 26(11)] investigated four different methods of preparing the superconducting compound PbMo S. The authors contend that the presence of oxygen during the preparation process affects the material's superconducting transition temperature T. Preparation methods 1 and 2 use techniques that are designed to eliminate the presence of oxygen, and methods 3 and 4 allow oxygen to be present. Five observations on T. (in ®K) were made for each method, and the results are as follows: Preparation Method Transition Temperature T°K) 14.8 14.8 14.7 14.8 14.9 14.6 15.0 14.9 14.8 14.7 12.7 11.6 12.4 12.7 12.1 14.2 14.4 14.4 12.2 11.7 (a) Is there evidence to support the claim that the presence of oxygen during preparation affects the mean transition tem- perature? Use a = 0.05. (b) What is the P-value for the F-test in part a)? (c) Analyze the residuals from this experiment. (d) Find a 95% confidence interval on mean T when method 1 is used to prepare the material. Source DF P-value Factor Error

Answer 1

Answer:

a)

For the given data, Using one way ANOVA

Treatments Total w 5 5 ΣΧ 61.5 66.9 276.4 Mean 14.8 14.8 12.3 13.38 13.82 x2 1095.22 1095.3 757.31 902.09 3849.92 Std.Dev. 0.0707 0.1581 0.4637 1.3198 1.2581

Source SS MS Between- treatments 22.124 7.3747 F= 14.84583 Within- treatments 7.948 0.4967 Total 30.072 19 The f-ratio value is 14.84583. The p-value is .00007. The result is significant at p<.05.

b) P- value = 0.00007

c)

Normal Probability Plot (response is Response) +---------------------------------------------------- + --------- ---------- --- ------- ---- ------ ---- -------- ------------------- ---- +----------------+--- --- ------- -- --- --- ------- ! --- ! ! --------- 60 +------- ! +--- ---+---+---+--- ----------- TF--- ------T--- --------- 30tf------ --- --- --- ---T /1 7 20 --------- ---+------- --SA------- Percent ------マートニーー ー ーート-------+- - - - ------ -----------+- ! ! ! ! ! ! - ---------------- --- ----------- --- --- ---+- -- -- ------- ------T -- -- ----- --- ---T- ---------------- -------+- 10 +-------+---+ --+- +--- -------------------- --- --- ---+- 5 +---------- T-Sf-----------------------------------+---+- 20151.0 -0.5 0.0 Residual 0.5_10_1.5

Versus Fits (response is Response) Residual -1.5- -2.0-4 12.0 12.5 13.0 13.5 Fitted Value 14.0 14.5 15.0 The normal probability plot of the residuals plot of transition temperature is not normal. And the residual versus fits reveals model adequacy.

d)

formula for the 100(1-a) percent confidence interval on the mean of the ith treatment is Jottakam),/MS, From the data we have the following values: 71. = 14.8, MS, = 0.797,n = 5, a = 4 Note that 10.025.4(5-1) = 10.025,16 = 2.12.

Therefore, the 95% confidence interval on the mean Te when method 1 is used to prepare the material is 7.10.025.16MS/n = 14.8+ 2.12 x 0.797/5 = 14. 80.8464 13.9536 54 315.6464