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Homework answers / question archive / In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit cards

In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit cards

Statistics

In a survey of 1430 undergraduate students, 1087 reported that they had one or more credit

cards.

a. Provide a 90% confidence interval for the proportion of all college students who have at

least one credit card.

b. Provide a 95% confidence interval for the proportion of all college students who have at

least one credit card.

c. Assuming all else held constant, as the confidence level increases does the confidence

interval get wider, narrower, or stay the same?

 

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Answer:

x = 1087

n = 1430

p =x/n = 0.76

standard error, SE = sqrt(p(1-p)/n)

SE = sqrt(0.76(1-0.76) / 1430)

= 0.0113

a.

alpha,a = 1-0.90 = 0.10

Za/2 = Z0.05= 1.645

confidence interval:

p +/- [Za/2 * SE]

0.76 +/- 0.0186

( 0.7416 , 0.7787 )

b.

alpha,a = 1-0.95 = 0.05

Za/2 = Z0.025= 1.96

confidence interval:

p +/- [Za/2 * SE]

0.76 +/- 0.0221

( 0.7380 , 0.7823 )

c.

as the confidence level increases, the confidence interval get wider

 

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