Two marathon training procedures are tried for comparison purpose

Two marathon training procedures are tried for comparison purpose

Subject: Mathematics    / Statistics
Question

Two marathon training procedures are tried for comparison purposes. Their efficacy is to be determined in a marathon race. Assume race times are given in minutes. Use?=0.058?=0.058for all calculations.

The following results were observed:. The data is given in the file below.

Download .csv file

(a) Do the populations appear to be normal? Hint: use a probability plot to decide
A. Yes, procedure A appears to be normal but procedure B does not appear to be normal

B. Yes, Both procedure A and procedure B appear to be normal

C. Yes, Both procedure A and procedure B appear to be non-normal

D. No, Both procedure A and procedure B appear to be normal

E. Yes, procedure B appears to be normal but procedure A does not appear to be normal

F. No, neither procedure A appears to be normal nor procedure B appears to be normal

(b) Choose the most appropriate statistical hypotheses to see which procedure results in longer marathon times (be very careful in how you formulate your hypothesis, this one is tricky! Use the sample data to make any assumptions necessary.)
A.H0:?1=?2HA:?1??2H0:?1=?2HA:?1??2

B.H0:?1=?2HA:?1<?2H0:?1=?2HA:?1<?2

C.H0:?D=0,HA:?D<0H0:?D=0,HA:?D<0

D.H0:?D=0,HA:?D>0H0:?D=0,HA:?D>0

E.H0:?1=?2HA:?1>?2H0:?1=?2HA:?1>?2

F.H0:?D=0,HA:?D?0H0:?D=0,HA:?D?0

(c) Using technology available to you, test to see if the variances are equal or not?
A. They appear to be equal.

B. There appears to be more variation in the 2nd procedure then in the 1st.

C. There appears to be more variation in the 1st procedure then in the 2nd.

D. There appears to be an unequal amount of variation in the 2nd procedure then in the 1st.

(d) Report the p-value of the test you ran in (c) use at least three decimals in your answer (this is from Levene’s test).

P-value =equation editorEquation Editor

(e) Test the statistical hypotheses in (b) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use at least two decimals in your answer (from your test of middle).

Test Statistic =equation editorEquation Editor

(f) Determine thePP-value for this test, to at least three decimal places (from your test of middle).

P=P=equation editorEquation Editor

(g) Based on the above calculations, we should

reject/not reject

the null hypothesis.