The paper \"Analysis of the Flat vs. Hole Entry\" cited in Example 16.6 also gav

Question

The paper "Analysis of the Flat vs. Hole Entry" cited in Example 16.6 also gave the data below on time from water entry to first stroke (below) and initial velocity. The authors of the paper used signed- rank tests to analyze the data.

a. Use a level 0.01 test to decide whether there is a significant difference in mean time from entyr to first stroke for the two entry methods.

b. do the data suggest a difference in mean intitial velocity for the two entry methods? Use a level 0.05 signed-rank test.

TIME FROM ENTRY TO FIRST STROKE CHART

INITIAL VELOCITY CHART

Swimmer 1 2 3 4 5 6 7 8 9 10 Hole 1.18 1.10 1.31 1.12 1.12 1.23 1.27 1.08 1.26 1.27 Flat 1.06 1.23 1.20 1.19 1.29 1.09 1.09 1.33 1.27 1.38

Explanation / Answer

a)

p-value for two-tail is 0.666 > 0.01

hence we fail to reject the null hypothesis

t-Test: Two-Sample Assuming Equal Variances hole flat Mean 1.194 1.213 Variance 0.007071111 0.011712222 Observations 10 10 Pooled Variance 0.009391667 Hypothesized Mean Difference 0 df 18 t Stat -0.438396692 P(T<=t) one-tail 0.333157481 t Critical one-tail 1.734063607 P(T<=t) two-tail 0.666314962 t Critical two-tail 2.10092204

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