7. the owner of the west end kwick 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. (a) calculate the sample proportion. what is the value of the population proportion? (b) develop a 95 percent confidence interval for the population proportion. (c) interpret your findings.

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12-12-2022
Mathematics

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7. the owner of the west end kwick 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. (a) calculate the sample proportion. what is the value of the population proportion? (b) develop a 95 percent confidence interval for the population proportion. (c) interpret your findings.

Answer :

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Tutorconsortium423 Tutorconsortium423 · Answer 1 · 2022-12-18T06:32:10-05:00

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

Confidence Interval: What is it?

In frequentist statistics, a confidence interval is the range of estimates for an unknown quantity. 95% is the most frequent confidence level used when calculating confidence intervals, however 90% and 99% are also occasionally used.

a)85 out of 100 paid at the pump using credit card

Thus,

p = proportion of customers who paid at the pump using credit card

= 85/100

= 0.850

Estimated Value of the population proportion = 0.850

b)

Given:

p' = 0.85 ....... Sample Proportion

n = 100 ....... Sample Size

For 95% Confidence interval

α = 0.05, α/2 = 0.025

From z tables of Excel function

Z = [tex]\frac{p'-p}{\sqrt{p(1-p)/n} }[/tex]

we find the z value

z = (0.025) = 1.96

We take the positive value of z

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

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