Question

1. An article in Materials Research Bulletin investigated four different methods of preparing the superconducting compound PbMo6S8. The authors contend that the presence of Oxygen during the preparation process affects the material’s superconducting transition temperature. Preparation methods 01 and 03 use techniques that are designed to eliminate the presence of Oxygen, and methods 03 and 04 allow Oxygen to be present. Five observations on Transition Temperature were made for each method, and the results are given in the table:

Preparation Method	Transition Temperature (Kelvin)
Method 01	14.8	14.8	14.7	14.8	14.9
Method 02	14.6	15	14.9	14.8	14.7
Method 03	12.7	11.6	12.4	12.7	12.1
Method 04	14.2	14.4	14.4	12.2	11.7

1. Write down the Null and Alternative hypotheses to test if the presence of Oxygen affects the Transition Temperature. Define all the terms used.   

2. What is the calculated Ftest statistic?                                                                                                                

3. What are the critical F value and the rejection region of H0 at α=5% ?                                         

4. Test the hypotheses using the test statistic / critical value method (use your answers to (b), and (c)). Clearly interpret the test result in the context of the problem.

What is the P value for the test? Test the hypotheses using the P value. Do you get the same answer as (d)? If your answer is different, clearly interpret it.

Answer 1

a) Here we want to test,

H0 : There is no significant effect of presence of Oxygen on Transition Temperature.

Vs

H1 : There is significant effect of presence of Oxygen on Transition Temperature.

Our data is like this,There are four levels of one factor.Factor is Preparation method.Therefor we use One way ANOVA To test oue hypotheses.

Preparation Method	Transition Temperature (Kelvin)
Method 01	14.8	14.8	14.7	14.8	14.9
Method 02	14.6	15	14.9	14.8	14.7
Method 03	12.7	11.6	12.4	12.7	12.1
Method 04	14.2	14.4	14.4	12.2	11.7

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Row 1	5	74	14.8	0.005
Row 2	5	74	14.8	0.025
Row 3	5	61.5	12.3	0.215
Row 4	5	66.9	13.38	1.742
ANOVA
Source of Variation	SS	df	MS	Cal.F	P-value	F crit
Between Groups	22.124	3	7.374667	14.84583	0.000070	3.238872
Within Groups	7.948	16	0.49675
Total	30.072	19

If Cal.F > F crit Then reject H0 at 5 % level of signifiacance.

b) Here we can see that cal.F (14.84)>F crit(3.23). Therefor we reject H0 at 5 % level of significance.

c) If P value is less than 0.05 then we reject H0 at 5% level of singificancde. Here we can see thet P-value(0.00007)is less than 0.05. Therefor we reject Ho at 5% level of significnace.

d) By using Critical value method and P-value method conclusion is same.

Conclusion : There is significant effect of presence of Oxygen on Transition Temperature.