A. Create a real world scenario of a study with a population mean and a population standard deviation. Include the information that a random sample of a given size (greater than 30) was selected from the population. b. Check the conditions for the assumptions about the sampling distribution.

c. Draw, label and describe the sampling distribution in context.

The t-score has the same interpretation as the z-score. It measures how far in standard deviation units \stackrel{-}{x} is from its mean μ. For each sample size n, there is a different Student’s t-distribution. The degrees of freedom, n – 1, come from the calculation of the sample standard deviation s. Remember when we first calculated a sample standard deviation we divided the sum of the squared deviations by n − 1, but we used n deviations \left(x-\stackrel{-}{x}\text{values}\right) to calculate s. Because the sum of the deviations is zero, we can find the last deviation once we know the other n – 1 deviations. The other n – 1 deviations can change or vary freely. We call the number n – 1 the degrees of freedom (df) in recognition that one is lost in the calculations. The effect of losing a degree of freedom is that the t-value increases and the confidence interval increases in width.

Properties of the Student’s t- Distribution 0.05, 95% level of confidence, we find the t-value of 1.96 at infinite degrees of freedom.

Step-by-step explanation:

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step-by-step explanation: