Question

A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey​ players' birthdates are not uniformly distributed throughout the​ year? Use the level of significance α=0.01.

Hockey League Players' Birth Month

Birth Month	​January-March	​April-June	​July-September	​October-December
Frequency	61	56	25	32

1. What are the null hypothesis and alternative​ hypotheses?

A. H0​: The distribution of hockey​ players' birth months is not uniformly distributed.

H1​: The distribution of hockey​ players' birth months is uniformly distributed.

B. H0​: The distribution of hockey​ players' birth months is uniformly distributed.

H1​: The distribution of hockey​ players' birth months is not uniformly distributed.

C. H0​: The distribution of hockey​ players' birth months is uniformly distributed.

H1​: More hockey players are born in the first half of the year than the second half.

D. H0​:The distribution of hockey​ players' birth months is uniformly distributed.

H1​: More hockey players are born in​ January-March than​ October-December.

2. Compute the expected counts for each birth month. The total number of hockey players is 174.

Birth Month	Observed Count	Expected Count
​January-March	61	_______
​April-June	56	_______
​July-September	25	_______
​October-December	32	_______
		​(Round to two decimal places as​ needed.)

3. What is the test​ statistic?___________

4. ​P-value=________What is the​ P-value of the​ test?

​(Round to three decimal places as​ needed.)

5. Based on the​ results, do the hockey​ league's players' birth months follow a uniform​ distribution? Use the level of significance α=0.01.

A. Yes​, because the calculated​ P-value is less than the given α level of significance.

B. No​, because the calculated​ P-value is greater than the given α level of significance.

C. Yes​, because the calculated​ P-value is greater than the given α level of significance.

D. No​, because the calculated​ P-value is less than the given α level of significance.

Answer 1

The statistical software output for this problem is:

Hence,

1. Hypotheses: Option B is correct.

2. Expected frequency of each cell = 174/4 = 43.5

Hence,

The complete table will be:

Birth Month	Observed Count	Expected Count
​January-March	61	43.5
​April-June	56	43.5
​July-September	25	43.5
​October-December	32	43.5

3. Test statistic = 21.54

4. P - value = 0.000

5. Option A is correct.