Question

Birthdays of hockey players: In Malcolm Gladwell’s book "Outliers" he shares the work of Canadian psychologist Roger Barnsley, who noticed that a disproportionately high percentage of elite ice-hockey players have birthdays between January and March. A group of statistics students would like to test if this is true for the Los Angeles Kings 2010-2015 rosters (22 out of 57). After debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value. They test the hypotheses LaTeX: H_0H 0: LaTeX: p=0.25p = 0.25 versus LaTeX: H_aH a: LaTeX: p>0.25p > 0.25. They use a significance level of 0.05. Their calculated test statistic is 2.37. Using the applet (at the top of this Checkpoint), what is the P‐value?

a. P‐value = 0.009
b. P‐value = 0.991
c. P‐value = 0.018
d. P‐value = 0.05

Answer 1

The P-value is 0.009.

Explanation:

We are given that after debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value.

We are given that the following hypothesis below;

Null Hypothesis,
`H_0` : p = 0.25

Alternate Hypothesis,
`H_A` : p > 0.25

Now, the test statistics that was used here for the above hypothesis would be;

T.S. =
`\frac{\hat p-p}{\sqrt{(\hat p(1-\hat p))/(n) } }` ~ N(0,1)

Also, the test statistics given to us is 2.37.

SO, the P-value of the test statistics is given by the following formula;

P-value = P(Z > 2.37) = 1 - P(Z
`\leq` 2.37)

= 1 - 0.99111 = 0.00889 ≈ 0.009

The above probability is calculated by looking at the value of x = 2.37 in the z table which has an area of 0.99111.

Therefore, the required P-value is 0.009.