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

Null Hypothesis (Ho): Males and females can equally make a quarter spin for the same length of time

Alternative Hypothesis (Ha):

Males can make a quarter spin longer than females can.

Data Collection Process•Simple random sample (size 40)

Selection bias-convenience sampling

•40 20 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)

6.549 9.671 11.314 13.300 17.766

Box Plot (females)

4.132 6.650 8.471 9.989 11.469

Numerical DataMale..

X=11.464

Sx =2.912

The distribution of the lengths of quarter spins is slightly skewed right, with a 5 #summary of [6.549, 9.671, 11.315, 13.300, 17.766] with no outliers.

Female…

X=8.298

Sx =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, 11.469] with no outliers.

Hypothesis testHo: um =uf

Ha: um >uf

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. SRSm, SRSf (assume)

2. 10nm < Nm

10nf < Nf

(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

Nm=20

N f=20

X m =11.464

X f =8.298

S m =2.912

S f =2.171

Alpha level=.05

Test statistics/p-values

t= xm –xf

sm2 + sf

2

nm nf

t = 3.166

2.912 2+ 2.1712

20 20

t=3.89

U D =0 x D=3.166UD =0 XD =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 3.166 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