Razorback realtors (rr) has apartment complexes in fayetteville that primarily rent to university of arkansas students. historically, 85% of tenants pay their rent on time. rr wants to be paid on time but also wants to students improve their credit score. since late payments negatively impact a tenant’s credit score, rr would like to decrease late payments in the future. a new program was implemented where if a tenant was not late with their rent during a six-month period, then rr would be give them a $50 wal-mart gift card. after six months of the program, 44 out of 50 tenants paid their rent on time. what is the p-value?

p-value=  0.27760

Step-by-step explanation:

Hello!

The RR apartment complex wants to decrease the proportion of tenants that pay their rent late. For this, they implemented the 6month pay on time and receive a Wal-Mart $50 gift card program.

If the historical proportion of tenants that pay on time is 85%, then the proportion of tenants that are late with their rent is 15%

If they want to test whether the proportion of the tenants that pay late decreased with the new program, the hypothesis is:

H₀: ρ ≥ 0.15

H₁: ρ < 0.15

α:?

The statistic is:

Z=       ^ρ - ρ     ≈ N(0;1)

    √[(ρ(1 - ρ))/n]

If 44 out of 50 paid on time, this means that 6 paid late. Since for this hypothesis we are testing the proportion of people that paid late, these 6 tenants will be our number of "success"

The sample proportion is: ^ρ= 06/50 = 0.12

Z=      0.12 - 0.15     = -0.59

   √[(0.15*0.85)/50]

The p-value is one-tailed (left) as the test:

P(Z ≤ -0.59) = 0.27760

I hope you have a SUPER day!