Question

NBA players: Michael wants to investigate whether the distribution of his classmates’ favorite NBA players of all time is different from the one reported by NBA. He randomly surveys his classmates. The table below contains the percentages reported by NBA and the observed counts from his random sample.

Player	LeBron James	Kobe Bryant	Steph Curry	Michael Jordan	Others
NBA %	20%	30%	15%	19%	16%
Observed Counts	23	28	10	15	11

a. If the percentages are as reported by NBA, then what is the degrees of freedom for the test statistic?

b. If the percentages are as reported by NBA, then what is the p-value for this hypothesis test?

c. Michael wants to carry out a statistical inference procedure for this scenario using the χ2 -distribution. Which of the following conditions must be met? (Select all that apply)

- The difference in all calculated proportions must be at least 5.

- The sample size must be at least 30 or the population data must be normally distributed.

- There must be at least 10 successes and 10 failures for each level of the categorical variable.

- The observations must be independent.

- There must be an expected count of at least 5 for each level of the categorical variable.

- There must be at least 3 levels of the categorical variable.

Answer 1

Player	Observed Count	Expected Proportion	Expected Count	(O-E)^2/E
LeBron James	23	0.2	0.2*87 = 17.40	1.8023
Kobe Bryant	28	0.3	0.3*87 = 26.10	0.1383
Steph Curry	10	0.15	0.15*87 = 13.05	0.7128
Michael Jordan	15	0.19	0.19*87 = 16.53	0.1416
Others	11	0.16	0.16*87 = 13.92	0.6125
Total Count =	87		χ2 = Σ(O-E)^2/E =	3.4076

Degrees of Freedom = n-1 = 5-1 = 4

P-value = 0.4921 [Obtained using MS Excel function =CHISQ.DIST.RT(3.4076,4)]

The following conditions must be met:

The observations must be independent.

There must be an expected count of at least 5 for each level of the categorical variable.