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 help 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?

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

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