* Conducting an appropriately designed experiment/study to test the notion that males can make a quarter spin longer than females*

Null Hypothesis (H o ): Males and females can equally make a quarter spin for the same length of time Alternative Hypothesis (H a ): Males can make a quarter spin longer than females can.

Data Collection Process Simple random sample (size 40) Selection bias-convenience sampling males 20 females To reduce the effect of any lurking variables… One method to spin quarter (use index of one and the thumb of the other hand) Same quarter (every coin is shaped differently) Flat smooth surface (angular surface may cause the spin to shorten or fall off the desk) Proper calibrated instrument (stopwatch) (prevent measurement bias) Time measured in seconds/milliseconds

dAta suMmaRieS 00:06:549 00:11:363 00:06:692 00:010:144 00:08:232 00:11:878 00:13:723 00:08:000 00:13:717 00:14:583 00:12:883 00:15:783 00:10:981 00:12:877 00:17:766 00:10:285 00:11:093 00:11:266 00:09:197 00:12:264 00:07:352 00:06:747 00:08:580 00:09:969 00:04:781 00:07:832 00:06:553 00:09:333 00:06:514 00:10:612 00:09:208 00:04:132 00:11:469 00:10:009 00:05:370 00:11:324 00:11:000 00:07:428 00:08:361 00:09:379 males FEMALES

Graphical Data Box plot (males) Box Plot (females)

Numerical Data Male.. X= S x =2.912 The distribution of the lengths of quarter spins is slightly skewed right, with a 5 #summary of [6.549, 9.671, , , ] with no outliers. Female… X=8.298 S x =2.171 The distribution of the lengths of quarter spins for females is slightly skewed left, with a 5 #summary of [4.132, 6.650, 8.471, 9.989, ] with no outliers.

Hypothesis test H o : u m =u f H a : u m >u f where u is the population avg as length of quarter spin This is a two sample means problem with unknown. Use 1 tailed t procedure with df=19. 1.SRS m, SRS f ( assume ) 2.10n m < N m 10n f < N f (assume that there’re at least 200 males and 200 females respectively) 3. Assume each individual spin independent 4. Little skew ness and no outliers N m =20 N f =20 X m = X f =8.298 S m =2.912 S f =2.171 Alpha level=.05

Test statistics/p-values t= x m –x f s m 2 + s f 2 n m n f t = t=3.89 U D =0 x D =3.166 U D =0X D =3.166 Bell Curve: P value is 0.

Conclusion If there were no difference in the lengths of the quarter spins between males and females, then the probability of obtaining the sample difference of or something more extreme would be essentially zero. Therefore there is sufficient evidence to show that males can spin longer than females can at 5%.

Selection Bias: Convenience Sampling (mostly students from stats class) Data has slight skew ness Calculations are not accurate and they only represent a sample of the population