Answer:
a)x₁ = 24 business owners plan to provide a gift this year
b) p-value = 0,0017
c)p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease
Step-by-step explanation:
a) Sample size 80
proportion p₁ = 30 % p₁ = 0,3
Then x₁ = 80*0,3
x₁ = 24 business owners plan to provide a gift this year
b) Hypothesis Test
Null Hypothesis H₀ p₁ = 0,45
Alternative Hypothesis Hₐ p₁ < 0,45
p₁ = 0,3 then q₁ = 1 - 0,3 q₁ = 0,7
z(s) = ( p₁ - 0,45 )/ √p₁* q₁ / n
z(s) = - 0,15 / √0,002625
z(s) = - 0,15 / 0,05123
z(s) = - 2,9279
b)From z-table we find p-value = 0,0017
c) If α = 0,05 ( significance level ) as
p-value < α we have to eject H₀ And support the claim that the proportion of business owners providing gifts has decrease
= 7.071