# Quantative Research Methods: Sample Size, Confidence Interval

Question 1:

As a sample size approaches infinity, how does the student's t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain.

Question 2:

A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is the initial hunch? Would one claim with 95% confidence that the mayor will win a majority of the votes? Explain.

https://brainmass.com/statistics/central-limit-theorem/200190

#### Solution Preview

1. As the sample size increases, the t-distribution approaches the normal distribution. As a sample size approaches infinity, the student's t distribution is equal to the normal z distribution.

When a researcher draws a sample from a normal distribution, the sample distribution is normally distributed.

If a population is normal with mean M and standard deviation s, the sampling distribution of sample mean is also normally distributed

If the Population is not Normal we can apply the Central Limit Theorem: The central limit theorem states that the distribution of sample means is ...