How to do a sign test

2. In an investigation to compare the accuracy of Crackshot and Fastfire
12-bore shotguns in clay pigeons shooting, ten competitors each fired
100 shots with each make of gun. Their scores are shown in the table
below.
Competitor A B C D E F G H I J
Crackshot 93 99 90 86 85 94 87 91 96 79
Fastfire 87 91 86 87 78 95 89 84 88 74

3. Hypothesis
(Crackshot – Fastfire)
HO - Population median difference of the
Crackshot gun being more accurate for
clay pigeon shooting = 0
H1 – Population median difference of the
Crackshot gun being more accurate for
clay pigeon shooting> 0

4. Test Statistic...
- - - - - - - - - -
= + = + = + = - = + = - = + = + = + = +
2- and 8+

5. ...Test Statistic
X~B (10,0.5)-(probability always =0.5)
P(X<2)=0.0547
0.0547>0.05
Therefore Accept H0

6. Conclusion
There is not sufficient evidence to suggest
at the 5% significance level that
Crackshot is more accurate when clay
pigeon shooting then Fastfire. So we
accept the null hypothesis and reject the
alternative hypothesis.