Question

You need to compute a 90% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.4? (Use 7.0 as an estimate of the population standard deviation from prior studies.) Use Table 1. (Round intermediate calculations to 4 decimal places. Round "z-value" to 3 decimal places. Round up your answer to the nearest whole number.)

Answer 1

As per the given confidence interval, the sample size is 102.

The term confidence interval in math is referred as  the mean of your estimate plus and minus the variation in that estimate.

Here we have given that you need to compute a 90% confidence interval for the population mean.

And we need to find the sample size.

While we looking into the given question, we have identified the following values,

Confidence interval = 90% = 0.09

mean = 1.4

Then the sample size is calculated as,

In order to find this one we have to find the critical value of z for 90% confidence level is,

=> z = 1.645

Now, we have to calculate the value of n as,

=> z x σ / √n

when we apply the value on it, then we get,

=> 1.645 x 1.4/√n

When we simplify this one then we get the value of n as 102.

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