Question

In: Statistics and Probability

NBA players ~ Michael wants to investigate whether the distribution of his classmates’ favorite NBA players...

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

Percentages

20%

30%

15%

19%

16%

Observed

Counts

Michael conducts the appropriate hypothesis test.

If, in fact, the percentages are as reported by NBA, then what is the p-value for this hypothesis test? Give your answer to 4 decimal places.

Based on the p-value that you calculated in the previous learning check question,which of the following describes the evidence to say that the distribution of Michael's classmates' favorite NBA players of all time is not the same as the one reported by NBA.

Question 7 options:

	Little evidence
	Some evidence
	Strong evidence
	Very strong evidence
	Extremely strong evidence

Solutions

Expert Solution

H0: The distribution of his classmates’ favorite NBA players of all time is same as the one reported by NBA.
H1: The distribution of his classmates’ favorite NBA players of all time is different from the one reported by NBA

n = 23 + 28 + 10 + 15 + 11 = 87

Expected count for Player if null hypothesis is true, Ei = n * pi

E1 = 87 * 0.2= 17.4
E2 = 87 * 0.3 = 26.1
E3 = 87 * 0.15= 13.05
E4 = 87 * 0.19= 16.53

E5 = 87 * 0.16 = 13.92

Chi-square test statistic =

= 3.407592

Degree of freedom = k-1 = 5-1 = 4

P-value = P( > 3.407592) = 0.4921

Since P-value is greater than alpha = 0.05, we fail to reject the null hypothesis and the distribution of Michael's classmates' favorite NBA players of all time is not the same as the one reported by NBA has Little evidence

orchestra answered 1 year ago

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