Suppose the manager of a shoe store wants to determine the current percentage of customers who are males. How many customers should the manager survey in order to be 92% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who are males?
z0.10 | z0.05 | z0.04 | z0.025 | z0.01 | z0.005 |
---|---|---|---|---|---|
1.282 | 1.645 | 1.751 | 1.960 | 2.326 | 2.576 |
Use the table of values above.
Solution :
Given that,
= 0.5
1 - = 1 - 0.5 = 0.5
margin of error = E = 5% = 0.05
At 92% confidence level the z is ,
Z/2 = 1.751 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.751/ 0.05)2 * 0.5 * 0.5
= 306.6
Sample size =307 ROUNDED
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