Question

assume that a sample is used to estimate a population mean u. use the given confidence level and sample data to find the margarine of error. assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal please send a sample standard deviation.

Answer 1

First, we have to find the critical value. Because the sample is big enough (more than 30 data), we use the z-distribution.

The alpha value to look for in a z-distribution table is calculated as:

$\alpha=1-c=1-0.95=0.05$

Where c is the confidence leven, which is 95% or 0.95 in the given exercise.

Now, wer look for a z-distribution table, and the critical value for alpha=0.05 is:

$criticalValue=1.95996$

Finally we have to multiply the standard deviation by this critical value. The standar deviation is calculated as follow:

$SE=\frac{202}{\sqrt{51}}=28.28566$

Finally, we multuply the SE by the critical value:

$28.28566*1.95996=55.44$

If we round the answer is the second option 56.8.