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Quantative Research Methods: Sample Size, Confidence Interval

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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.

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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 ...

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Quantitative Research Methods: Estimating Population Mean

A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled "3 pounds." Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.

a. What is the estimated population mean?

b. Determine a 95 percent confidence interval for the population mean.

A study of 25 graduates of four-year colleges by the American Banker's Association revealed the mean amount owed by a student in student loans was $14,381. The standard deviation of the sample was $1892. Construct a 90 percent confidence interval for the population mean. Is it reasonable to conclude that the mean of the population is actually $15,000? Tell why or why not.

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