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The manager of a department store wants to determine the proportion of customers who use the store's credit card when making a purchase. What sample size should he select so that at 96% confidence the error will not be more than 10%?

a. 106
b. 76
c. 1
d. There is not enough information given to determine the sample size

Respuesta :

Answer:

Option A) 106  

Step-by-step explanation:

We are given the following in the question:

Confidence level = 96%

Margin of error = 10%

Formula:

Sample size, n =

[tex]n = \dfrac{z^2p(1-p) }{E^2}[/tex]

[tex]z_{critical} \text{ at 0.04 level of significance } = 2.05[/tex]  

Since, we are not given any proportion, we take

[tex]p = 0.5[/tex]

Putting all the value, we get,

[tex]n = \dfrac{(2.05)^2(0.5)(1-0.5) }{(0.10)^2}\\\\n = 105.0625\\n \approx 106[/tex]

Thus, the correct answer is

Option A) 106

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