Question

An author argued that more basketball players have birthdates in the months immediately following July​ 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with​ January: 390​, 392​, 360​, 318​, 344​, 330​, 322​, 496​, 486​, 486​, 381​, 331 . Using a 0.05 significance​ level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency? Do the sample values appear to support the​ author's claim?

Answer 1

There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

Explanation:

In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

`\chi^(2)=\sum{((O-E)^(2))/(E)}`

The values are computed in the table.

The test statistic value is
`\chi^(2)=128.12`.

The degrees of freedom of the test is:

n - 1 = 12 - 1 = 11

Compute the p-value of the test as follows:

p-value < 0.00001

*Use a Chi-square table.

p-value < 0.00001 < α = 0.05.

So, the null hypothesis will be rejected at any significance level.

Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same​ frequency.