Question

A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).

a. (2 pts) What is the appropriate test?

b. (1 pt) State the null hypothesis:

c. (1 pt) State the alternative hypothesis:

d. (2 pts) Find the critical value:

e. (1 pt) Calculate the obtained statistic:

f. (2 pts) Make a decision:

g. (2 pts) What does your decision mean?

Answer 1

0.5 (b) a) One proportion z test Null hypothesis;HO: p= Alternative hypothesis;H1: p> sample proportion: 0.5 c) 0.85714 Here,x= 12 72 Sample size: n= 14 Standard error: P(1-P) 0.13363 = 72 a= 0.05 Level of significance: Critical value: 1.64 (d) Decision rule: Reject Ho if z > 1.64 Critical region : Z> 1.64 Test statistic: 20 = p-p p(1-P) 2.67 e) n p-value: For z= 2.67 The right tailed p-value is 0.0038 using r code f)Decision: Since p-value <a, we reject HO g)Conclusion : The coin is weighted for heads