# 4. A random sample of n measurements was selected from a population with unknownmean μ and known standard deviation σ. Calculate a 95% confidence interval for μ foreach of the following situations:b. n-200,x-: 102,02-22

Question
Step 1

Computing the 95% confidence interval for population mean:

Here, the sample size is 75, sample mean x-bar is 28 and sample variance is 12. The population standard deviation is known here. Therefore, z-test can be used here. Let µ be the true population mean.

Let x bar be the sample mean, σ be the population standard deviation and n is the sample size.

The 100(1-α) % confidence interval of µ is,

Step 2

The confidence level is 95%. Therefore, the significance level, α = 0.05 and the z value corresponding to α/2 is 1.96.

Therefore the 95% confidence interval of mean is,

Step 3

b.

Computing the 95% confidence interval for population mean:

Here, the sample size is 200, sample mean x-bar is 102 and population variance is 22. The population standard deviation is known here. Therefore, z-test can be used here. Let µ be the true population mean.

Let x bar be the sample mean, σ be...

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