Question

A marketing firm is trying to estimate the proportion of potential car buyers that would consider purchasing a hybrid vehicle. The firm would like their pilot study to have a margin of error that is no more than 3.5%. How many people should be in this study to meet this goal at the 98% confidence level? Critical Value: Your answer should contain 3 decimal places. Sample Size:

Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3.5% = 0.035

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.326 / 0.035)2 * 0.5 * 0.5

=1104.13

Sample size = 1104

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