Question

3) The owner of the KiKi Fill Gas Station wishes to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80 paid at the pump. 1. Estimate the value of the population proportion. 2. Develop a 95% confidence interval for the population proportion. 3. Interpret your findings

Answer 1

i) Estimate the value of the population proportion = 0.8

ii) 95% confidence interval for the population proportion

(0.7214 , 0.8784)

iii) Lower bound = 0.7214

upper bound = 0.8784

Explanation:

Step(i):-

Given sample size 'n' = 100

Given data he surveys 100 customers and finds that 80 paid at the pump

sample proportion

`p = (x)/(n) = (80)/(100) = 0.8`

Step(ii):-

95% confidence interval for the population proportion is determined by

`(p^(-) - Z_(\alpha ) \sqrt{(p(1-p))/(n) } , p^(-) + Z_(\alpha ) \sqrt{(p(1-p))/(n) })`

Level of significance

∝ =0.05

Z₀.₀₅ = 1.96

`(0.8 - 1.96 \sqrt{(0.8 X 0.2))/(100) } , 0.8 + 1.96 \sqrt{(0.8 X 0.2)/(100) })`

On calculation , we get

(0.8 - 0.0784 , 0.8 + 0.0784)

(0.7214 , 0.8784)

Conclusion:-

95% confidence interval for the population proportion

(0.7214 , 0.8784)