1.)If the population standard deviation ( s) is known then we use it in calculating the z-statistic as follows.
z= [Xbar - m ] / [ s/ sqrt(n) ]

On the other hand if population standard deviation is unknown, we substitute the sample standard deviation (s) in place of population standard deviation in calculating the z-statistic.
z= [Xbar - m ] / [ s/ sqrt(n) ]

Exercise:
A soda bottling machine is filling 32 oz. soda cans. We observe the machine filling 35 bottles (picked at random) and obtain the following data:

As a bottler we want to know if the machine was underfilling. Setup Null and Alternate hypotheses to test if average amount of soda in each can is less than 32 oz. Please test the hypothesis using a = 0.05. What can you conclude from all this?

Solution Summary

This solution provides a null and alternative hypothesis and calculates the test statistic to compare with the level of significance in order to accept or reject the null hypothesis.

... Since population is large, Standard deviation of sample means distribution =Population standard deviation/sqrt(sample size) = 2.2361/sqrt(15) = 0.5774. ...

... treatment, test whether these samples represent populations that are ... with a mean of 44, (b) a sample of 1 ... The general population of individuals has a mean of 40 ...

... was -1 .) The sample mean was 0.6 hours, and the standard deviation was 1.6 hours ... Assume that the sample is drawn from a normally distributed population. ...

... are unknown, we use independent sample t test ... We want to test whether the populations have the ... This is a test for two population standard deviation/variance so ...

... for a problem that has 2 sample populations greater than ... of 40 observations is selected from one population. ... mean is 102 and the sample standard deviation is 5 ...

... with a standard deviation that the population standard deviations of lifetimes in these two countries can be estimated by the sample standard samples used were ...

... NA p (sample proportion): NA Since sample size is large Z test is used with sample standard deviations as an estimate of population standard deviation . ...

... Details. Confidence Interval Estimate for the Mean. Data Population Standard Deviation 1.5 Sample Mean 6.5 Sample Size 100 Confidence Level 95%. ...