Question

We want to estimate the population mean within 16, with a 90% level of confidence. The population standard deviation is estimated to be 45. How large a sample is required? (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.)

Sample size

Answer 1

Solution :

The sample size required to estimate the population mean with 90% confidence level is given as follows :

Where, σ is population standard deviation, E is margin of error, Z(0.10/2) is critical z-value to construct 90% confidence interval and n is sample size.

Since, we want to estimate the population mean within 16, therefore the margin of error E = 16.

σ = 45 and Z(0.10/2) = 1.645

Hence, the required sample size is,

On rounding to nearest whole number we get,

n = 21

Hence, the required sample size is 21.

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