Question

In an early home game, an NBA team made 72.34 percent of their 94 free throw attempts. In one of their last home games, the team had a free throw percentage equal to 78.16 percent out of 87 attempts. Do basketball teams improve their free throw percentage as their season progresses? Test the appropriate hypotheses for free throw percentages, treating the early season and late season games as random samples. Use a level of significance of .10.

(a-1)	Assume ππ1 is the early proportion of free throws and ππ2 is the later proportion. Choose the correct null and alternative hypotheses.

a.

H₀: ππ₁ – ππ₂ ≤ 0 vs. H₁: ππ₁ – ππ₂ > 0

b.

H₀: ππ₁ – ππ₂ = 0 vs. H₁: ππ₁ – ππ₂ ≠ 0

c.

H₀: ππ₁ – ππ₂ ≥ 0 vs. H₁: ππ₁ – ππ₂ < 0

	a
	b
	c

(b-1)

Use Excel to calculate the exact p-value. (Round the number of free throws to the nearest integer; and round your answer to 4 decimal places.)

p-value

Answer 1

The statistical software output for this problem is:

Hence,

a - 1) H₀: ππ₁ – ππ₂ ≥ 0 vs. H₁: ππ₁ – ππ₂ < 0

b - 1) p - Value = 0.1827