A 95% confidence interval for a population mean is computed from a sample of size 400. Another 95% confidence interval will be computed from a sample of size 100 drawn from the same population. Choose the best answer to fill in the blank: The interval from the sample of size 400 will be approximately as the interval from the sample of size 100. Multiple Choice

The interval from the sample of size 400 will be approximately One -half as wide as the interval from the sample of size 100

Step-by-step explanation:

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the 95% confidence interval is dependent on the value of the margin of error at a constant sample mean or sample proportion

Generally the margin of error is mathematically represented as

Here assume that is constant so

=>  

=>  

So  let   and

=>  

=>  

=>  

So From this we see that  the confidence interval for a sample size of 400 will be half that with a sample size of 100

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