A hockey team is convinced that the coin used to determine the order of play is

Question

A hockey team is convinced that the coin used to determine the order of play is weighted for tails. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted for tails, and it shows up tails 11 times. Test this hypothesis (use alpha=.01).

(2 pts) What is the appropriate test?

(1 pt) State the null hypothesis:

(1 pt) State the alternative hypothesis:

(2 pts) Find the critical value:

(1 pt) Calculate the obtained statistic:

(2 pts) Make a decision:

(2 pts) What does your decision mean?

Explanation / Answer

The appropriate test is t - test.

Below are the null and alternate hypothesis,
H0: p <= 0.5
H1: p > 0.5

degrees of freedom = 14 - 1 = 13

Here pcap = 11/14 = 0.7857
SE = sqrt(0.5*0.5/14) = 0.1336
test statistics value,
t = (pcap - p)/SE = (0.7857 - 0.5)/0.1336 = 2.1385

Critical value for significance level of 0.01 for 13 df = 2.650

As test statistics is less than critical value, we fail to reject the null hypothesis.

This means there is no evidence that the coin is weighted for tails.

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