Question

A bank wants to evaluate which credit card would be more attractive to its customers, one with a high interest rate for unpaid balances but no annual fee or one with a low interest rate for unpaid balances for an annual fee of $50. Foe a random sample of 100 of its 52,000 customers, 40 said they prefer the one that has an annual fee. Would you conclude statistically that more people prefer the card with no annual fee?

Test the hypothesis that customers are more likely to prefer the card with no annual fee than if they were randomly selecting for the significance level of 0.05.

Answer 1

given data are:-

sample size (n) = 100

number of customers who said they prefer the one that has an annual fee = 40

x = number of customers who said they prefer the one that has no annual fee = (100-40) = 60

sample proportion () = 60/100 = 0.6

we will do 1 proportion Z test.

hypothesis:-

where, p is the population proportion of customers who said they prefer the one that has no annual fee.

test statitistic be:-

p value be:-

[ from standard normal table]

decision:-

p value = 0.0228 < 0.05 (alpha)

we reject the null hypothesis.

conclusion:-

there is sufficient evidence to support that customers are more likely to prefer the card with no annual fee than if they were randomly selecting for the significance level of 0.05

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