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What are some of the assumption to use to determine a confidence interval for the population mean with an unknown standard deviation? Provide examples.
Define the confidence interval for a population proportion and indicate how it is estimated with an example.
What are the factors that determine the sample size? How is sample size calculated for estimating the population mean? Provide examples.
When population standard deviation is unknown then we need to use t-confidence interval.
Eiether populaiton should be normally distributed or sample size should be atleast 30 to apply CLT.
The sample should be simple random sample from population.
Obervations should be independent.
Suppose we have
And let it is given that populaiton is normally distributed.
Since there 16 data values in the sample so degree of freedom is df=16-1=15 and critical value of t for 95% confidence interval, using excel function "=TINV(0.05,15)" is 2.131.
The required confidence interval is
Therefore, a 95% confidence interval for the mean is (24.19, 27.81).
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