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A cellphone company provider has the business objective of wanting to estimate

A cellphone company provider has the business objective of wanting to estimate the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 135 of the subscribers would upgrade to a new cellphone at a reduced cost. A. At the 0.05 level of significance, is there evidence that more than 20% of the customers would upgrade to a new cellphone at a reduced cost? B. How would the manager in charge of promotional programs concerning residential customers use the results in (a)?
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1 Answer

H0 : ρ ≤ .20
H1 : ρ > .20 (Claim)
 
α = 0.05
One-tailed test(because H1 ">". If H1 "=", then would be two-tailed test)
X=135
n =500     
^  
ρ= 135/500=0.27     
^
q = 365/500=0.73
 
Using Graphing Calculator TI-83: Go to STATS, TESTS, 5:1-PropZTest, ρ0: .20, X: 135, n: 500, prop >ρ0, Calculate.
 
Since p-value = 4.557E-5 = 0.00004557 which is less than the level of significance α=0.05. Therefore, reject H0 and support the claim that more than 20% of customers would upgrade to a new cell phone at a reduced cost.
The manager would go ahead and promote new cellphones at a reduced rate based on these results.