Question

# In a study using 15 samples, and in which the population standard deviation is not known,...

In a study using 15 samples, and in which the population standard deviation is not known, state the distribution that should be used to calculate confidence interval and the associated parameter(s) and why this distribution is used.

In this case sample size is 15 and population standard deviation is unknown.so we will use the sample standard deviation to construct the confidence interval here. This statistic follows a

t distribution with df=n-1 =14

To conduct any testing procedure we assume that the sampling distribution of the test statistic follows a normal distribution . But in that case the sample size should be sufficiently large and the population standard deviation is known.

But whenever sample size is not so high and population standard deviation is unknown then we use the sample standard deviation in place of population standard deviation to construct our test statistic to conduct the testing procedure.

And the parameter of the t distribution depends on the sample size. It is called degrees of freedom or df. In this problem df of t distribution is =15-1 = 14 .

So here we will use t​​​​​​14 distribution.

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