Question

3. You will need to download the data file "Wet Suits" from Sakai. Researchers are interested in finding out if wet suits allow a swimmer to swim faster. Researchers measured the speed (in meters per second) of swimmers both with and without a wet suit. The results of the study are shown in the table. A normal probability plot indicates the differences d = with - without are approximately normally distributed. Swimmer With 1.57 1.47 1.42 1.35 1.22 1.75 1.64 1.57 1.56 1.53 1.49 1.51 Without 1.49 1.37 1.35 1.27 1.12 1.64 1.59 1.52 1.5 1.45 1.44 1.41

Answer 1

A. The Sampling Method used in this study is dependent since the same group of swimmers are monitored for with and without wet suits.

B.

immer 1 2 0.07 1.27 with without difference 1.57 1.49 0.08 1.47 1.37 0.1 1.42 1.35 1.35 0.08 1.22 1.12 0.1 1.64 0.11 1.64 1.59 0.05 1.57 1.52 0.05 1.56 0.06 1.53 1.45 1.49 I 1.44 | 0.05 1.51 1.41 0.1 1.75 B00VA 1.5 0.08 11 12 Mean 0.0775 standard 0.021794 deviation

C.

I t-Test: Paired Two Sample for Means Mean Variance Observations Pearson Correlation Hypothesized Mean Differe Variable 1 Variable 2 1.50666667 1.429167 0.0185697 0.019899 12 12 0.98824278 df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 11 12.3181509 4.4427E-08 1.79588482 8.8854E-08 2.20098516

D.

Null Hypothesis, H₀: There is no significant difference in the average speed of the swimmers with and without the wet swim suits i.e.
mul = mu2

Alternative Hypothesis, H₁: Wet swim suits allows swimmers to swim faster i.e.  
mul> mu2

Test Statistics: Under Ho,

  
P]P8_ T- U PPS -7

From our summary table in part C, t = 12.3181509 and t-critical value = 1.79588482

Test-Criteria: We may reject H₀ at 5% level of significance if t calculated > t-critical value or if p-value>0.05

SInce, t-calculated = 12.3182 > t-critical=1.79588 and

p-value = 4.4427E-08 < 0.05 so we reject H₀ at 5% level of significance and conclude that wet swim suits help swimmers to swim faster.